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+Fred works the night shift in a refrigerator storage warehouse. It's not very exciting work, but Fred has ways to pass the time when nobody's around. +For example, lifting fridges turns out to be an amazing bodybuilding method! +

+ +

+The warehouse consists of N sections in a row, numbered from 1 to N. +In each section i, there are initially Fi fridges, all arranged in a single stack. +The sections are intended to be separate from one another, and only accessible from the outside. +To that end, each pair of adjacent sections are separated by a wall, for a total of N-1 walls. +However, these walls don't stretch all the way to the ceiling, and aren't necessarily all of the same height. +The wall between sections i and i+1 has a height of Hi fridge-heights (Fred has come to measure everything relative to fridge dimensions). +Fred's favourite pastime involves climbing over these walls to get between the warehouse's sections! +

+ +

+Fred will begin by entering the warehouse in some section, carrying in some number of new fridges from the outside (yes, he's become strong enough to carry multiple fridges in his arms at once). When he's currently in a certain section s and is carrying f fridges, he may perform any of the following actions: +

+ +

+ +

+Fred's goal is to visit all N sections at least once each. +He just needs to decide which section he should initially enter and how many additional fridges he should bring from the outside. +He has M such possible starting situations in mind, the ith of which involves him beginning in section +Xi while carrying Yi fridges. +For each hypothetical starting situation, please help Fred determine whether or not he will be able to visit all N sections! +

+ + +

Input

+ +

+Input begins with an integer T, the number of warehouses Fred works at. +
For each warehouse, there is first a line containing the space-separated integers N and M. +
Then follows a line with the N space-separated integers F1 through FN. +
Then follows a line with the N - 1 space-separated integers H1 through HN-1. +
Then, M lines follow, the ith of which contains the space-separated integers Xi and Yi. +

+ + +

Output

+ +

+For the ith warehouse, print a line containing "Case #i: " followed by +a string of M characters, the ith of which is "Y" if Fred can visit all N sections from the ith starting situation, or "N" otherwise. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 90
+2 ≤ N ≤ 8,000
+1 ≤ M ≤ 8,000
+0 ≤ Fi ≤ 100,000
+1 ≤ Hi ≤ 100,000
+1 ≤ XiN
+0 ≤ Yi ≤ 1,000,000,000
+

+ +

+The sum of N across all T test cases is no greater than 80,000.
+The sum of M across all T test cases is no greater than 80,000. +

+ + +

Explanation of Sample

+ +

+In the first case, the warehouse is arranged as follows: +

+ + + +

+If Fred begins in section 1 holding 0 fridges, he can't climb over the wall to visit section 2, whereas if he's holding 1 fridge, he can place it in section 1 and then climb over. +On the other hand, if he begins in section 2, he can climb over the wall to visit section 1 using the existing fridge, regardless of whether he's holding any himself. +

+ +

+In the second case, consider the first starting situation, in which Fred begins in section 3 holding 4 fridges: +

+ + + + +

+He could begin by placing 3 of his fridges in section 3, and using them to climb over the wall into section 4 while still holding 1 fridge: +

+ + + +

+He could then place his remaining fridge in section 4, climb back to section 3, pick up a fridge there, and climb over to section 2 while holding that 1 fridge: +

+ + + +

+Finally, he could place his final fridge in section 2 and climb over to section 1: +

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+25 0 +73 102663 +60 10246 +85 120613 +76 120613 +67 34037 diff --git a/2019/finals/cold_storage.md b/2019/finals/cold_storage.md new file mode 100644 index 0000000000000000000000000000000000000000..c82463a41a8d5f569b91b870671964c90cd9090f --- /dev/null +++ b/2019/finals/cold_storage.md @@ -0,0 +1,97 @@ +Fred works the night shift in a refrigerator storage warehouse. It's not very +exciting work, but Fred has ways to pass the time when nobody's around. For +example, lifting fridges turns out to be an amazing bodybuilding method! + +The warehouse consists of **N** sections in a row, numbered from 1 to **N**. +In each section _i_, there are initially **Fi** fridges, all arranged in a +single stack. The sections are intended to be separate from one another, and +only accessible from the outside. To that end, each pair of adjacent sections +are separated by a wall, for a total of **N**-1 walls. However, these walls +don't stretch all the way to the ceiling, and aren't necessarily all of the +same height. The wall between sections _i_ and _i_+1 has a height of **Hi** +fridge-heights (Fred has come to measure everything relative to fridge +dimensions). Fred's favourite pastime involves climbing over these walls to +get between the warehouse's sections! + +Fred will begin by entering the warehouse in some section, carrying in some +number of new fridges from the outside (yes, he's become strong enough to +carry multiple fridges in his arms at once). When he's currently in a certain +section _s_ and is carrying _f_ fridges, he may perform any of the following +actions: + + * Pick up a fridge from section _s_'s stack of fridges, if it's non-empty. This decreases the number of fridges in that stack by 1, and increases _f_ by 1. + * Add a fridge that he's carrying onto section _s_'s stack of fridges, if he's carrying at least one fridge. This decreases _f_ by 1, and increases the number of fridges in that stack by 1. + * Climb onto section _s_'s stack of fridges and jump over a wall into an adjacent section, if the number of fridges in that stack is at least as large as the height of that wall (in fridge-heights). This decreases or increases _s_ by 1. + +Fred's goal is to visit all **N** sections at least once each. He just needs +to decide which section he should initially enter and how many additional +fridges he should bring from the outside. He has **M** such possible starting +situations in mind, the _i_th of which involves him beginning in section +**Xi** while carrying **Yi** fridges. For each hypothetical starting +situation, please help Fred determine whether or not he will be able to visit +all **N** sections! + +### Input + +Input begins with an integer **T**, the number of warehouses Fred works at. +For each warehouse, there is first a line containing the space-separated +integers **N** and **M**. +Then follows a line with the **N** space-separated integers **F1** through +**FN**. +Then follows a line with the **N** \- 1 space-separated integers **H1** +through **HN-1**. +Then, **M** lines follow, the _i_th of which contains the space-separated +integers **Xi** and **Yi**. + +### Output + +For the _i_th warehouse, print a line containing "Case #_i_: " followed by a +string of **M** characters, the _i_th of which is "Y" if Fred can visit all +**N** sections from the _i_th starting situation, or "N" otherwise. + +### Constraints + +1 ≤ **T** ≤ 90 +2 ≤ **N** ≤ 8,000 +1 ≤ **M** ≤ 8,000 +0 ≤ **Fi** ≤ 100,000 +1 ≤ **Hi** ≤ 100,000 +1 ≤ **Xi** ≤ **N** +0 ≤ **Yi** ≤ 1,000,000,000 + +The sum of **N** across all **T** test cases is no greater than 80,000. +The sum of **M** across all **T** test cases is no greater than 80,000. + +### Explanation of Sample + +In the first case, the warehouse is arranged as follows: + +![]({{PHOTO_ID:668467847037494}}) + +If Fred begins in section 1 holding 0 fridges, he can't climb over the wall to +visit section 2, whereas if he's holding 1 fridge, he can place it in section +1 and then climb over. On the other hand, if he begins in section 2, he can +climb over the wall to visit section 1 using the existing fridge, regardless +of whether he's holding any himself. + +In the second case, consider the first starting situation, in which Fred +begins in section 3 holding 4 fridges: + +![]({{PHOTO_ID:3188801037832284}}) + +He could begin by placing 3 of his fridges in section 3, and using them to +climb over the wall into section 4 while still holding 1 fridge: + +![]({{PHOTO_ID:268184757597716}}) + +He could then place his remaining fridge in section 4, climb back to section +3, pick up a fridge there, and climb over to section 2 while holding that 1 +fridge: + +![]({{PHOTO_ID:281442036550128}}) + +Finally, he could place his final fridge in section 2 and climb over to +section 1: + +![]({{PHOTO_ID:657561505101033}}) + diff --git a/2019/finals/cold_storage.out b/2019/finals/cold_storage.out new file mode 100644 index 0000000000000000000000000000000000000000..9c6ec631b681fa45b59131a9f0c0cdc32909e5fb --- /dev/null +++ b/2019/finals/cold_storage.out @@ -0,0 +1,124 @@ +Case #1: NYYY +Case #2: YNYNY +Case #3: NYYY +Case #4: NYNNYYNNY +Case #5: NYNNNYNYYN +Case #6: NYYNNNNNYYNYNNNYNYYYYYYYYNNYNN +Case #7: NNYYYYYNNYN +Case #8: YNNNNY +Case #9: YNNNNNYNY +Case #10: YNYNYYYYY +Case #11: YYYNNNNNYNNN +Case #12: YYNNNNNNNNYY +Case #13: NNYNNNY +Case #14: NNYYYYYNNYN +Case #15: NNNYYNNYYNYY +Case #16: YYNNNNY +Case #17: NYYNNNNYYNN +Case #18: NYYNYNYYY +Case #19: YNNNNNYN +Case #20: NNYN +Case #21: YYNNYNY +Case #22: NNYY +Case #23: YY +Case #24: NNNYNNYNYYNYYYYYYYNNNYYYNYYNNNNNNYYNYNYYNNNYYNNNNYYYYNNYYNYNNNYNYYYNYYNNNYYYNNYNNNNYYYNYYYYNNNNNYNYYNYYYNYNYNYYNNYNNYYNYNYNNYNNYYNYNNNNNYYNYYNYYNYNNYNYYYNYYNYNNYYNNYYYYYNYNYYYYNNYYYNYYYNYNYYYYYYYYYYNNYYNYNNNNNNYYYYYYNNYYNYNYYNYNNNNNYNNYNNNYNNYNYNYYYNNNNNNYYNYYNNYNYYNYNNNYNNYNNNYNNNNNYYNYNYNYYYYYYYYYNNNNNNYYNYNYYYNYNNYYNYNYNNYYYNNYYYYYYNNNYYYNNNYYYNNYNYNNYYYNYNNNNNNYYYYNNNNNYYNNYNYNYNNNNNNYYNYYYNNYNNNNYYNNNNNYNNYNYYYYYNYYYNNNNYNYNYYNNNYNNYNYNNYYNNYYNNNYYYYNYNNYYNYNYYYYYNYNYYNNNYYNYNYYNYNNNYYYYYNYYYYYNNNNNYYYYYNNNNYYNNNNNNNYNYYNNYNYNNNYYNYYNNNNNYNYYYNNYNNYYYNNNYYNYNYNYYYYNNNYYYYYYNYYNYNNYNYYNYYNYNNYYYYYYNNNYNYYNYNYYYYYNYNYNYNNYYNNYNNNNNYYNNYYNYYNYYNYYYYNNYNYNYNNYNYYYYYNNNNYYYNNNYNNNYYNNYNYNNYNYYYYNYYNYYYYNNYNNYNNYNYYNYNYNYNNYYYNYNNNYYYNYYYNNNNNNYNNYYYYNNNYNYNNNYYYNNYYNYNYNNYYNNNNNYNNNYYYYNYNYNYYNNYYYYNNYNNNYYNNYYNYNYNYNNNYYNNNNNNNNNYNNNNYNYYNYNNNNYNNNYNNNYYNNNNNYYNYYNNNNNNYNYNNNYNNYYYYNYNNNNYNNNYYYYYYYNNYNNYYNYYNYYNNYYYNNYYYYYYNYYNNNNYYYYYNNYNYNNYYNYYNNNNNYNNNNYNYNNNNYYYNYYNYNYYNNYYNNYYYNNYYYYYNNNYNNNYNYNNYYYYYNYYYNNYNYNYNNYNYYYYNYNNNNYYNNYYYYNYYYNYYYYYNNNYNYNNNNNYNNNYNYNNYYYNNYYYNNNNNYNNYYYYYNNNNYYYNYYNNYNYNNYNYNNYNYYNNYNYNNNNNYYNNYYNNYYNNNNYNNNYYNNNYYYNYNYYNNNYYYNNNYYNYYYYYYYNYNYNYYYYYNYNYYNYNYNYNYNNYYYYNYNYYYNYYYNNYNYYNNNYYNNNYYNYYNNYNYYYNYNYYYNNYNYYNNNNYYNNNYNNNNNNNYNYNNYYYYNYNYYYYYNNNNNNYYNYNYYNYYNNNNNYYYNNYYNNNNYNYNYNYNNNNNNNYYYYNNYNNNYNNNNYYYNYYYYYNNYNNYNNNYYYYNNYNNYNYNYNNYYNNYYYYNNYYNNYYYYNNNNNYNNYYYNNYNNNYNYYYYNNNYYNYYYYYNYNNYYNYYNYYYYNYNYYNYNNYNNNYNNNYNYYNYNNNNNNNNNYYYNNYNYNYYNNYNNNYYYNYNNYYNYYNNNNYYNYYYNYYNNNYNYYYNNYNYYNNYNYNYNNYYYNNYNNYNYYYYNYNYNYYYYNYNNYYYNYNYNNYNNNYYYYYYYNNYYYYNYNYYNNYNNNYNYYYYNYNYNNYNNYNNYNYYYYYYYYYNYNNYNNNNNNNNYYYYNNYNNYYNYNYYYNNNYNNNNYNYNNYNNYYYNYYYYYNYNNNYNNNYNYNYNYNNYNYYYYYNYNYYYYYNNYYYNNYYYNNNNYYYNYYYYNNYYNNNNYYYYNNNNYNYNNYYNNNNYNYNNNYNNYNNNNNNNNNYYNYYYYNYNYYYNNNNNYYYNYYNNYNNNNNNYNNYYNYNNNYYYNYNNYNNYNYNNYNYYNNNNNYYYNNNNNYNYYYNYYNYNYNNNYYNYNNYNYYYYNNYNYYYNYNNYYNNYNNNYNYNNNYYYNNYYYNYYYNYNYNNNYYNNNYNYYYYNNNNNYYNYNYNNYNNNNNNNYYYYYYNNNNYYYNNNYYNYNNNNNNNYYYYYNYNYNNNYNNNYYNYYYYNNNYYYYYNYYNNNNNNNNNYYYNNNYNNYNYYYYNYNYYYNYYYNNYYNNYNYYYNNNNYYYYYNYNYYNNYNNYYYNNYYYYYNYYNYYYYYYYNYYNYNNYYYNYNYYYNYNYYYNNNNYNYYYYYYNNYNNYYYNYNYNYNYNNNYNYNNYYYNYYYNYYYYNYYNYYYYNYNNYYNYYYNYNYYYNNNNYNYYYNYNNNYYNNYYNNYNNYNYNYNNYYYNYYYNNNYYNYNNYNYNNYYNYNNYNYYNYYNNNYYYNYYYNYNNNNYYNYYYYNNYNYNNYNYNNYNYNNYYYNNNYYYYYYYYNYNYYNNYNNNYNYNNNNNNYNNNYYYNNYNYNNNYYNYYYNYNNYNNYNNNYYYNYNYNNNYNNNYNNYYYYYNYNNNYYNNYYYNYNYYNYYNNYYYYNYNYYNYNYYYNNNYNNNYYYYNNNNYYYNNNNYNYYNNYNYNNYNYYNNNNYNNYYNNYNNNYNNYNNYNNYYYYYNNNNYNYYYNYYNYYYYYNNNYNYYYNNYYYYNNNYYNNNYYNNNYYNNNNNYNYYYYNNYNNNYYYYNNYYYYYYYNYNNNYYYYYYNNNYNNNNNNYYNYYNYNNYNNNNYYYNYNYNNNNNYNNYNYYYYYNNYNYNYNYYNNNNYNNYNYYNNNYYYNYNNNYNNYYYNNNNYYNNYNNNYYYNNNYYNYNNNNNYYNYNNYYYYNNNNNYNYYNYNNNYYNNNYYYNYYNNNNYYYYYNNNNYNYYNNNYYYYYYNYYYNYNYYYNNYNNYNYYYYNNNYYNYYNNNNNNYYNYNYYNYNYYYYYNYYNYYNYYYYYYNYYYNNYYNYNYNNYNYYYNNYNYNYYYNNNYYNNNYNNNYNYNNNNNNYYYNNNYYNYNNNNNNYNYNNYYNNNNNYYYYNNYYNYYNNNYNNYNYYNYNNYNYNYYYNYYYYNYNYYYNNNNYYYNNYNNNYNYYNNYNYNYNNYYYNYYNYYYYYNNNYNNYYYNNYYNYNNYYYYYYNYYNNYYNYNNNNYNNYYNYYNYYYYYNYYNYYNNNYYNNNYNYYNNYNNYYYYNYNYNNYYYNNNYYNYNYNYYNNYNYNYYYNYYNYYYYNNNYNYNYNNNNNYNYYYYNNYNNNNYYYYNNNYYYYYYYNYNYYYYNYNYNYYNYNNYYYNYNYNYYNNYNNNNYYYNYYNYNYNNYYYYYNNNYYNNYNYNYYYYNNYNYNYYYYNYNNYYNNNNYNNNNYYNYNNNNYYYNYYYNNNNYYNYYYNYYNYYNNNNYYYYNYYYNNNNNNNYYNNYNNYYYYNNNNYNNYYNYYYYYYNNYNNNYNYYNNYYNYYYNYNNNYYNYNYYYYNNYNNNNNNYNNYYYNYNNYYYNYYYNNYYYYNNNYNYYNYYYNYNYYNYNYNNNNNYYYNNYYYNYNNYYYYYNNNNYYNNYNYYNNNNNNNYNNNYNYNYYNYYNNNYNYYNYYNNYNYYNNYYYYYYYYNYYYYYNNYNYYYNYNNYNYYNNYYNYNNNNNNNNYYYNNYYYYNYNNYNYYNYYNNNYNNYNYYNNYNNYNNYNNNYNNNNNYNYNNNYNNNNYYYYYYYYYNNNYYYNYNNNNYNYNYYYYNNYNNNNNNNYYNYNYNNYYYYNYNNYNYNYYYYYYYNYNYNNYYNNYNYNNYYNNYYYNYYYNNYYYYYNYNYNNNYNNNYYYYYYNNNNYYNYYYNYYNYNNYYNYNNNYYYYYYNYNNYNYYYYNNNYNYNNYYNYNYYYYYNNYNNNYNNYNYNNYNYYYYYYYYNNNNNYNNYYYYNYNNNYYNYYYNYYYNNYNNYYYYYNYYNNNNNNNYNYYNNNYYNYYYYNYYNNYNNYNYNYYNNYYNNNNNYYYYYYYNNNYNYYYYYYYYNYYNNYNYYNNYNNYNNNNNYYNYYNYYYNYYNNYYNYYYYYNNNNNNNYYNNNNYYYYNNNYNYNYYNYNNNYNYYYNYNYYNYYNYYNYNYYYNYNNNNYNYNYYNNYNYNNYYNNNYYNNNYYYNNYNYNYNYYNNYNYYNNNNYYYYNYNNYYNNYNYYYYYNNYNNNNYNNYNYYYYNYYNNYNNNYNNNNYNNYNYNYYNNYNYYNNNNNNNNYNNNYNNNYNYYNNYYNYYNYYNYNNNNYNYYYNYNYYYNYNNYNNYNYYYYNYYYNYYYYNYNNYNNNNNYNYYYNNYYNYNYNNNNYYYNNNNNYYYNYYNYYYYNNNYYNNNYNNYYYYYNNYYNNYYNNNYNYNNYYNNNNNYNYYNYYNNYYYNYNYNYNYYYNYNYNNNNYNYYYYNYNNYNNNYNNYNNNNNNYNNYYNNNYYNYYNNYNNNNYYYYYYNYNYYNYNNNYNNYNYNYNNYNYNYNYNNYYNNYYNYNNYNNYYNYYYNNNNNNNNYYYNYYNNNNNNNYNNYNYYYNYYYYNNYNNNNNNNNNYNNNYYNNNYNNNNYYNNYYNYNNNNNNNNYYYNYNNYYYYYYNYNYNYNNNYNYYYNNNYYYYNYNYNNNYNNNYNYYNYNYYNYYNYNNNYNNYYYYYNNYNYYYNYYYNNYNYYNYNNYYYNNYYYNNYYYNYNNNYYNNYYYYYYNYNYYYYNNNNNYYYNYNNYNNNYNNNYNYNYNYNYYNNNNYNYYYYYNYNNYNNYYYNNYNNYNNYNNYYYYYYYNNNNYNNYYNYNNNNYNNNYYNYYNNYNYNNNYNNNNNNNNNNYYNNYNNNNYYNYYYNYNNNNNNYNYNYYNYNYYNYNYNYYNYYNNYYYNNYNYYYNNNYNNYNNYYNNNYYYNYYYNYNNYNYYNYYYYNYYYNYNNNNNYYYYYNNYYNNYYNYNYNYNNNYNYYNNYNNYNNNYYNNNNNYYNYYNNYNYYNNYYNNYNNYNNYYYNYNNYYNNNYNYYNNYYNYYYYYNNYNNYNYNYYNNNYNYYYNYNYNNNNYYYYNYYYNYNNNYNYYYYNNNNYYYYYYYYYYYYYYYNNNYYYYNNYYNNYYNYYNNYNNYNNNNYYNYYNNYYYNNNYNN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+Case #25: 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+Case #26: 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+Case #27: 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+Case #28: 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NYNNNNNNNYYYYNNNYNYYNYNYYYNYYYYNNYNYYYYNYNYYYYYYYNNYNNYYYNYYYYYYYYYYYYYNYNYYYYYNYNYYNYNNYNYYNNNN diff --git a/2019/finals/khajiit.cpp b/2019/finals/khajiit.cpp new file mode 100644 index 0000000000000000000000000000000000000000..1da444f01a91fb80d437528d432f6ca643eca18d --- /dev/null +++ b/2019/finals/khajiit.cpp @@ -0,0 +1,145 @@ +// Khajiit +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x < 0 ? -x : x); } +template T Sqr(T x) { return(x * x); } +string plural(string s) { return(Sz(s) && s[Sz(s) - 1] == 'x' ? s + "en" : s + "s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int& x) { + char c, r = 0, n = 0; + x = 0; + for (;;) { + c = GETCHAR(); + if ((c < 0) && (!r)) + return(0); + if ((c == '-') && (!r)) + n = 1; + else if ((c >= '0') && (c <= '9')) + x = x * 10 + c - '0', r = 1; + else if (r) + break; + } + if (n) + x = -x; + return(1); +} + +bool ReadLL(LL& x) { + char c, r = 0, n = 0; + x = 0; + for (;;) { + c = GETCHAR(); + if ((c < 0) && (!r)) + return(0); + if ((c == '-') && (!r)) + n = 1; + else if ((c >= '0') && (c <= '9')) + x = x * 10 + c - '0', r = 1; + else if (r) + break; + } + if (n) + x = -x; + return(1); +} + +#define MOD 1000000007 +#define LIM 1000005 + +int N, M; +char X[LIM], Y[LIM]; + +LL Solve(int s) { + int i; + LL sum = 0; + int hasA = 0, needsA = 0; + FoxR(i, M) { + if (X[s + i] == 'A') + hasA++; + if (Y[s + i] == 'A') + needsA++; + sum += Abs(hasA - needsA); + } + return(sum); +} + +int main() { + if (DEBUG) + freopen("in.txt", "r", stdin); + // vars + int T, t; + int i; + // testcase loop + Read(T); + Fox1(t, T) { + // input + Read(N), Read(M); + scanf("%s%s", &X, &Y); + // handle each spoke + LL ans = 0; + Fox(i, N) + ans += Solve(i * M + 1); + // output + printf("Case #%d: %lld\n", t, ans); + } + return(0); +} diff --git a/2019/finals/khajiit.html b/2019/finals/khajiit.html new file mode 100644 index 0000000000000000000000000000000000000000..c186329a0c69056992bd46ea64ff0a749f5beffe --- /dev/null +++ b/2019/finals/khajiit.html @@ -0,0 +1,97 @@ +

+The far-off land of Tamriel is brimming with opportunity! Opportunity for adventure, politics, romance... and, perhaps most importantly of all, commerce. +

+ +

+A group of Khajiit merchants, traditionally known for roaming the countryside selling their wares, have recently set up permanent bazaars in a number of towns. +Having gotten their cat-like paws on a large supply of raw amber and bronze, they're prepared to strategically work together to maximize their profits selling it! +

+ +

+One bazaar has been set up in each of N*M+1 towns. The towns are numbered from 0 to N*M, inclusive, +and are connected by roads in a hub-and-spokes arrangement, with town 0 in the center and N lines of M towns each arranged around it. +The ith such line consists of towns M*(i-1)+1 to M*i, inclusive, +connected together in order by M-1 roads (with one between towns M*(i-1)+1 and M*(i-1)+2, +another between towns M*(i-1)+2 and M*(i-1)+3, and so on). +For each line i, there is furthermore a road connecting its first town (M*(i-1)+1) to town 0. +Note that each of the N*M roads may be travelled in either direction, +and that each town may be reached from each other town by following a sequence of roads. +

+ +

+For example, if N=4 and M=2, the arrangement of towns and roads would look as follows: +

+ + + +

+Initially, the bazaar in each town i is stocked with either amber (if Xi = "A") or bronze (if Xi = "B"). +However, in order to satisfy demand, it should end up stocked with a potentially different ware, either amber +(if Yi = "A") or bronze (if Yi = "B"). +It's guaranteed that the number of bazaars initially stocked with amber is equal to the number of bazaars which should end up stocked with amber (consequently, the same holds true for bronze). +

+ +

+In order to accomplish their goal, the Khajiit merchants may repeatedly select a pair of towns which are directly connected by a road, and swap their bazaars' wares. +Please help them determine the minimum number of such swaps required for all N*M+1 bazaars to end up stocked with the required wares! +This is guaranteed to be possible for every possible valid input. +

+ + +

Input

+ +

+Input begins with an integer T, the number of Khajiit groups. +
For each group, there is first a line containing the space-separated integers N and M. +
Then follows a line with the length-(N * M + 1) string X, +the characters X0 through XN*M. +
Then follows a line with the length-(N * M + 1) string Y, +the characters Y0 through YN*M. +

+ + +

Output

+ +

+For the ith group, print a line containing "Case #i: " followed by +one integer, the minimum number of swaps required to stock all of the bazaars with the required wares. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 80
+1 ≤ N, M ≤ 1,000,000
+1 ≤ N * M ≤ 1,000,000
+

+ +

+The sum of N * M across all T test cases is no greater than 10,000,000. +

+ + +

Explanation of Sample

+ +

+In the first case, no swaps are required. +

+ +

+In the second case, bazaars 1 and 2 should swap their goods. +

+ +

+In the third case, the bazaars are initially set up as follows (with ones carrying amber marked in yellow, and ones carrying bronze marked in orange): +

+ + + + +

+The following sequence of 3 swaps could then be performed to arrive at the required configuration: +

+ +
+
+
diff --git a/2019/finals/khajiit.in b/2019/finals/khajiit.in new file mode 100644 index 0000000000000000000000000000000000000000..1b1a0a50b02b704e51a872f312bdaeee690eee09 --- /dev/null +++ b/2019/finals/khajiit.in @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:63da73bdb5a27d5fc5b6a9af3ef777ccdcf5b8f97d6e91e291b31d7d6f461e5c +size 12722187 diff --git a/2019/finals/khajiit.md b/2019/finals/khajiit.md new file mode 100644 index 0000000000000000000000000000000000000000..517210b686a4ec9b71581baff2e9985dad90b024 --- /dev/null +++ b/2019/finals/khajiit.md @@ -0,0 +1,84 @@ +The far-off land of Tamriel is brimming with opportunity! Opportunity for +adventure, politics, romance... and, perhaps most importantly of all, +commerce. + +A group of Khajiit merchants, traditionally known for roaming the countryside +selling their wares, have recently set up permanent bazaars in a number of +towns. Having gotten their cat-like paws on a large supply of raw amber and +bronze, they're prepared to strategically work together to maximize their +profits selling it! + +One bazaar has been set up in each of **N*****M**+1 towns. The towns are +numbered from 0 to **N*****M**, inclusive, and are connected by roads in a +hub-and-spokes arrangement, with town 0 in the center and **N** lines of **M** +towns each arranged around it. The _i_th such line consists of towns +**M***(_i_-1)+1 to **M***_i_, inclusive, connected together in order by +**M**-1 roads (with one between towns **M***(_i_-1)+1 and **M***(_i_-1)+2, +another between towns **M***(_i_-1)+2 and **M***(_i_-1)+3, and so on). For +each line _i_, there is furthermore a road connecting its first town +(**M***(_i_-1)+1) to town 0. Note that each of the **N*****M** roads may be +travelled in either direction, and that each town may be reached from each +other town by following a sequence of roads. + +For example, if **N**=4 and **M**=2, the arrangement of towns and roads would +look as follows: + +![]({{PHOTO_ID:291992558607686}}) + +Initially, the bazaar in each town _i_ is stocked with either amber (if **Xi** += "A") or bronze (if **Xi** = "B"). However, in order to satisfy demand, it +should end up stocked with a potentially different ware, either amber (if +**Yi** = "A") or bronze (if **Yi** = "B"). It's guaranteed that the number of +bazaars initially stocked with amber is equal to the number of bazaars which +should end up stocked with amber (consequently, the same holds true for +bronze). + +In order to accomplish their goal, the Khajiit merchants may repeatedly select +a pair of towns which are directly connected by a road, and swap their +bazaars' wares. Please help them determine the minimum number of such swaps +required for all **N*****M**+1 bazaars to end up stocked with the required +wares! This is guaranteed to be possible for every possible valid input. + +### Input + +Input begins with an integer **T**, the number of Khajiit groups. +For each group, there is first a line containing the space-separated integers +**N** and **M**. +Then follows a line with the length-(**N** * **M** \+ 1) string **X**, the +characters **X0** through **XN*M**. +Then follows a line with the length-(**N** * **M** \+ 1) string **Y**, the +characters **Y0** through **YN*M**. + +### Output + +For the _i_th group, print a line containing "Case #_i_: " followed by one +integer, the minimum number of swaps required to stock all of the bazaars with +the required wares. + +### Constraints + +1 ≤ **T** ≤ 80 +1 ≤ **N**, **M** ≤ 1,000,000 +1 ≤ **N** * **M** ≤ 1,000,000 + +The sum of **N** * **M** across all **T** test cases is no greater than +10,000,000. + +### Explanation of Sample + +In the first case, no swaps are required. + +In the second case, bazaars 1 and 2 should swap their goods. + +In the third case, the bazaars are initially set up as follows (with ones +carrying amber marked in yellow, and ones carrying bronze marked in orange): + +![]({{PHOTO_ID:266243124686458}}) + +The following sequence of 3 swaps could then be performed to arrive at the +required configuration: + +![]({{PHOTO_ID:637978470132709}}) +![]({{PHOTO_ID:950762542025264}}) +![]({{PHOTO_ID:635336360404128}}) + diff --git a/2019/finals/khajiit.out b/2019/finals/khajiit.out new file mode 100644 index 0000000000000000000000000000000000000000..617b2b3fee450194a67c3c72eb1d993aedc8b3fc --- /dev/null +++ b/2019/finals/khajiit.out @@ -0,0 +1,80 @@ +Case #1: 0 +Case #2: 1 +Case #3: 3 +Case #4: 6 +Case #5: 13 +Case #6: 36 +Case #7: 54 +Case #8: 0 +Case #9: 250000500000 +Case #10: 247439996515 +Case #11: 137532384990 +Case #12: 990173 +Case #13: 6712972 +Case #14: 30583 +Case #15: 19752 +Case #16: 12 +Case #17: 51000 +Case #18: 9446 +Case #19: 28856 +Case #20: 243 +Case #21: 62831 +Case #22: 219140 +Case #23: 75630 +Case #24: 75328 +Case #25: 1 +Case #26: 115571 +Case #27: 54768 +Case #28: 7181 +Case #29: 40292 +Case #30: 11064 +Case #31: 76372 +Case #32: 21252 +Case #33: 121615 +Case #34: 7480 +Case #35: 205037 +Case #36: 45380 +Case #37: 99952 +Case #38: 96162 +Case #39: 393152 +Case #40: 135921 +Case #41: 115531 +Case #42: 88951 +Case #43: 57276 +Case #44: 2922 +Case #45: 60962 +Case #46: 181620 +Case #47: 11094 +Case #48: 11835 +Case #49: 155512 +Case #50: 153429 +Case #51: 25614 +Case #52: 46346 +Case #53: 41740 +Case #54: 701 +Case #55: 179930 +Case #56: 346 +Case #57: 57312 +Case #58: 30808 +Case #59: 13601 +Case #60: 37852 +Case #61: 87552 +Case #62: 11455 +Case #63: 122374 +Case #64: 25883 +Case #65: 59589 +Case #66: 5149 +Case #67: 22447 +Case #68: 177181 +Case #69: 32399 +Case #70: 40144 +Case #71: 129059 +Case #72: 6285 +Case #73: 51006 +Case #74: 64574 +Case #75: 354972 +Case #76: 123528 +Case #77: 3483 +Case #78: 26835 +Case #79: 90120 +Case #80: 206821 diff --git a/2019/finals/little_boat_on_the_sea.html b/2019/finals/little_boat_on_the_sea.html new file mode 100644 index 0000000000000000000000000000000000000000..76495316613a028b4211c849f52079b9de517c60 --- /dev/null +++ b/2019/finals/little_boat_on_the_sea.html @@ -0,0 +1,77 @@ +

+Recently, Melody built a little boat, as cute as it could be. And she put a number of animals, two-by-two, on her little boat on the sea! +

+ +

+Melody's boat features N rooms, numbered from 1 to N. +The contents of the ith room are described by the string Ai. +If Ai = "-", then the room is empty, while otherwise the room contains an animal of species Ai +(where Ai is a case-sensitive alphanumeric string made up of lowercase letters "a"..."z", uppercase letters "A"..."Z", and digits "0"..."9"). +There are at most two animals of any given species on the boat. +

+ +

+There are N-1 corridors in the boat, the ith of which allows Melody and the animals to travel in either direction between rooms +Xi and Yi. Each room is reachable from each other room by following a sequence of corridors. +

+ +

+It's time for Melody's daily walk through her boat! She'd like to choose one room to start in and a different room to end in, and walk from the former to the latter. +She'll take the unique path which allows her to do so without visiting any room multiple times. Along the way, any time she finds herself in a room containing an animal +(including the starting or ending room), that animal will join her for the remainder of her walk. Normally, both Melody and the animals will keep quiet, which is just how she likes it. +However, if two animals of any given species ever end up joining her, they'll promptly make a racket talking to one another, which is no good! +As such, she'll refuse to take a walk which would result in encountering two of any species of animal. +

+ +

+For how many of the N*(N-1) possible ordered pairs of starting/ending rooms would it be possible for Melody to enjoy a quiet walk from one to the other? +

+ + +

Input

+ +

+Input begins with an integer T, the number of boats. +
For each boat, there is first a line containing the integer N. +
Then, N lines follow, the ith of which contains the string Ai. +
Then, N - 1 lines follow, the ith of which contains the space-separated integers Xi and Yi. +

+ + +

Output

+ +

+For the ith boat, print a line containing "Case #i: " followed by +one integer, the number of valid ordered pairs of starting and ending rooms for Melody's walk. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 95
+2 ≤ N ≤ 800,000
+1 ≤ Xi, YiN
+1 ≤ |Ai| ≤ 10
+

+ +

+The sum of N across all T test cases is no greater than 4,000,000. +

+ + +

Explanation of Sample

+ +

+In the first case, the 4 starting/ending room pairs (1, 2), (2, 1), (2, 3), and (3, 2) are valid. +On the other hand, the pairs (1, 3) and (3, 1) are not. For example, on the way from room 1 to room 3, a Fox would begin following Melody around in room 1, and upon being joined by another Fox in room 3, the two Foxen would begin making strange noises towards one another. +

+ +

+In the second case, both possible starting/ending room pairs ((1, 2) and (2, 1)) are no good, as they would involve encountering two talkative Turtles. +

+ +

+In the third case, both possible starting/ending room pairs will do, as no two animals of any given species can be encountered. +

+ diff --git a/2019/finals/little_boat_on_the_sea.in b/2019/finals/little_boat_on_the_sea.in new file mode 100644 index 0000000000000000000000000000000000000000..c98d0cc03a0d411ff72059577ab0ab0b1c34187b --- /dev/null +++ b/2019/finals/little_boat_on_the_sea.in @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:07006c7e87cc24203590a9edac2d350f17e74d530741b180136e90d265722196 +size 60455824 diff --git a/2019/finals/little_boat_on_the_sea.md b/2019/finals/little_boat_on_the_sea.md new file mode 100644 index 0000000000000000000000000000000000000000..ebc37ab866652b610bcc955450c39c0788287156 --- /dev/null +++ b/2019/finals/little_boat_on_the_sea.md @@ -0,0 +1,67 @@ +Recently, Melody built a little boat, as cute as it could be. And she put a +number of animals, two-by-two, on her little boat on the sea! + +Melody's boat features **N** rooms, numbered from 1 to **N**. The contents of +the _i_th room are described by the string **Ai**. If **Ai** = "-", then the +room is empty, while otherwise the room contains an animal of species **Ai** +(where **Ai** is a case-sensitive alphanumeric string made up of lowercase +letters "a"..."z", uppercase letters "A"..."Z", and digits "0"..."9"). There +are **at most two animals of any given species** on the boat. + +There are **N**-1 corridors in the boat, the _i_th of which allows Melody and +the animals to travel in either direction between rooms **Xi** and **Yi**. +Each room is reachable from each other room by following a sequence of +corridors. + +It's time for Melody's daily walk through her boat! She'd like to choose one +room to start in and a different room to end in, and walk from the former to +the latter. She'll take the unique path which allows her to do so without +visiting any room multiple times. Along the way, any time she finds herself in +a room containing an animal (including the starting or ending room), that +animal will join her for the remainder of her walk. Normally, both Melody and +the animals will keep quiet, which is just how she likes it. However, if two +animals of any given species ever end up joining her, they'll promptly make a +racket talking to one another, which is no good! As such, she'll refuse to +take a walk which would result in encountering two of any species of animal. + +For how many of the **N***(**N**-1) possible ordered pairs of starting/ending +rooms would it be possible for Melody to enjoy a quiet walk from one to the +other? + +### Input + +Input begins with an integer **T**, the number of boats. +For each boat, there is first a line containing the integer **N**. +Then, **N** lines follow, the _i_th of which contains the string **Ai**. +Then, **N** \- 1 lines follow, the _i_th of which contains the space-separated +integers **Xi** and **Yi**. + +### Output + +For the _i_th boat, print a line containing "Case #_i_: " followed by one +integer, the number of valid ordered pairs of starting and ending rooms for +Melody's walk. + +### Constraints + +1 ≤ **T** ≤ 95 +2 ≤ **N** ≤ 800,000 +1 ≤ **Xi**, **Yi** ≤ **N** +1 ≤ |**Ai**| ≤ 10 + +The sum of **N** across all **T** test cases is no greater than 4,000,000. + +### Explanation of Sample + +In the first case, the 4 starting/ending room pairs (1, 2), (2, 1), (2, 3), +and (3, 2) are valid. On the other hand, the pairs (1, 3) and (3, 1) are not. +For example, on the way from room 1 to room 3, a Fox would begin following +Melody around in room 1, and upon being joined by another Fox in room 3, the +two Foxen would begin making strange noises towards one another. + +In the second case, both possible starting/ending room pairs ((1, 2) and (2, +1)) are no good, as they would involve encountering two talkative Turtles. + +In the third case, both possible starting/ending room pairs will do, as no two +animals of any given species can be encountered. + diff --git a/2019/finals/little_boat_on_the_sea.out b/2019/finals/little_boat_on_the_sea.out new file mode 100644 index 0000000000000000000000000000000000000000..5da23f0ed91b1886b3bf038db175e394dc165b55 --- /dev/null +++ b/2019/finals/little_boat_on_the_sea.out @@ -0,0 +1,106 @@ +Case #1: 4 +Case #2: 0 +Case #3: 2 +Case #4: 8 +Case #5: 48 +Case #6: 358 +Case #7: 1801672158 +Case #8: 1892171288 +Case #9: 1851118504 +Case #10: 635640308616 +Case #11: 235104 +Case #12: 346054 +Case #13: 1984 +Case #14: 16584 +Case #15: 25254 +Case #16: 776864 +Case #17: 311244 +Case #18: 569040 +Case #19: 97144 +Case #20: 7112 +Case #21: 725062 +Case #22: 114124 +Case #23: 49252 +Case #24: 446268 +Case #25: 650854 +Case #26: 15922 +Case #27: 2902 +Case #28: 295858 +Case #29: 691768 +Case #30: 963564 +Case #31: 37720 +Case #32: 396818 +Case #33: 166556 +Case #34: 120910 +Case #35: 127884 +Case #36: 777402 +Case #37: 16368 +Case #38: 365376 +Case #39: 303266 +Case #40: 55382 +Case #41: 255716 +Case #42: 1092 +Case #43: 370480 +Case #44: 48566 +Case #45: 222910 +Case #46: 19270 +Case #47: 411790 +Case #48: 185492 +Case #49: 391326 +Case #50: 146310 +Case #51: 113264 +Case #52: 130156 +Case #53: 937168 +Case #54: 120118 +Case #55: 162184 +Case #56: 363434 +Case #57: 159916 +Case #58: 738966 +Case #59: 765880 +Case #60: 865888 +Case #61: 209644 +Case #62: 918060 +Case #63: 184 +Case #64: 193880 +Case #65: 652442 +Case #66: 393916 +Case #67: 238342 +Case #68: 176160 +Case #69: 3480 +Case #70: 811600 +Case #71: 84352 +Case #72: 431904 +Case #73: 680032 +Case #74: 166928 +Case #75: 968366 +Case #76: 31468 +Case #77: 507080 +Case #78: 131174 +Case #79: 1570 +Case #80: 21304 +Case #81: 53536 +Case #82: 289132 +Case #83: 654002 +Case #84: 12904 +Case #85: 33254 +Case #86: 315626 +Case #87: 212330 +Case #88: 473848 +Case #89: 558506 +Case #90: 710960 +Case #91: 533980 +Case #92: 555138 +Case #93: 3474 +Case #94: 639088 +Case #95: 121638 +Case #96: 218092 +Case #97: 603820 +Case #98: 616360 +Case #99: 89778 +Case #100: 20418 +Case #101: 144440 +Case #102: 766934 +Case #103: 28700 +Case #104: 558936 +Case #105: 128732 +Case #106: 905352 diff --git a/2019/finals/scoreboard.html b/2019/finals/scoreboard.html new file mode 100644 index 0000000000000000000000000000000000000000..ccd1d439b215ab802ea6d5dcd329810f8948cbe2 --- /dev/null +++ b/2019/finals/scoreboard.html @@ -0,0 +1,73 @@ +

+The 2019 Hacker Cup Finals have just concluded! There were N participants (numbered 1 to N), +including yourself (competing as participant 1), and M problems (numbered 1 to M). +

+ +

+Participant i solved problem j if Si,j = "Y", and otherwise they didn't solve it (if Si,j = "N"). +Problem i's point value is 2i, and each participant's score is the sum of the point values of the problems that they solved. +No two participants solved exactly the same set of problems, which also means that all participants have distinct scores. +

+ +

+Before the final results get announced, you have an opportunity to rearrange the M columns of the scoreboard S +into any permutation of problems 1 to M. +For example, if you swap columns 1 and 2, then everybody who had originally solved problem 1 will now be considered to have solved problem 2 +(thus earning 4 points for it rather than 2), and vice versa. +

+ +

+Of course, you'd like to use this opportunity to your benefit — it would be irresponsible to just let it pass by! +However, it would be too suspicious if you simply made yourself win the whole competition. +As such, you'd like to cause yourself to end up in 2nd place, such that you (participant 1) have exactly the second-highest score out of all N participants. +Now you just need to determine whether or not this is achievable... +

+ + +

Input

+ +

+Input begins with an integer T, the number of scoreboards. +
For each scoreboard, there is first a line containing the space-separated integers N and M. +
Then, N lines follow, the ith of which contains a length-M string, the characters +Si,1 through Si,M. +

+ + +

Output

+ +

+For the ith scoreboard, print a line containing "Case #i: " followed by +one character, either "Y" if you can end up in 2nd place, or "N" otherwise. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 200
+2 ≤ N ≤ 400
+1 ≤ M ≤ 400
+

+ +

+The sum of N * M across all T test cases is no greater than 1,000,000. +

+ + +

Explanation of Sample

+ +

+In the first case, there's only one possible permutation of problems: [1]. This results in you having a score of 2 and participant 2 having a score of 0, which puts you in 1st place rather than 2nd. +

+ +

+In the second case, if you preserve the original permutation of problems, [1, 2], you'll have a score of 2 while participant 2 has a score of 4, putting you in 2nd place, as required. +The permutation [2, 1] would have put you in 1st place instead. +

+ +

+In the third case, if you choose the problem permutation [2, 1], the 4 participants' scores will be 4, 0, 6, and 2, respectively. This puts you in 2nd place, as required. +The problem permutation [1, 2] would have put you in 3rd place instead. +

+ diff --git a/2019/finals/scoreboard.in b/2019/finals/scoreboard.in new file mode 100644 index 0000000000000000000000000000000000000000..420441fa0f64e7422c23edf07067c38523909f71 --- /dev/null +++ b/2019/finals/scoreboard.in @@ -0,0 +1,6224 @@ +228 +2 1 +Y +N +2 2 +YN +NY +4 2 +YN +NN +YY +NY +8 8 +NYNYNYNN +NYNNYYNY +YYNNNYYN +NYNYNNNN +YYYNYYYN +YNYNNYYN +YYNNNYNY +NYYNYYNN +8 8 +YNNYYNNY +NYNYYYNN +YNNYNNNY +NYNYYYNY +YNNNYNNN +NNNYYNNY +NYNYNYNY +NYNNNYNY +8 10 +NNYYNNYYNY +NYYNYNYYNY +NNYYYYYYNN +NYYYNYYYYY +NNYYYNYNNY +NNYNYNYYYY +YNYYNNYYYY +NYYYYNYNYY +8 10 +YYNNYNYNYN +YYNYYNNYYN +YNNNYYYNYY +YYYNYYYYNN +YYNNYNYYYN +NYNNYNYNYY +YYNNNYNYNN +YYNYYYNNYN +10 12 +YYYYNNYNYYNY +YNYNNNYNYYNY +YYNYNYYNYYNY +YYNNNNYNNYYY +YNYYNNYNYNNY +YYNYYYYNNYNY +YYNYNYYNNYYY +YYNYNYYNYYYY +YYNYYNYNNYNY +NYYYNNYNYNNY +3 4 +YYYN +NNYN +YNYN +2 2 +YN +NN +3 9 +YNYNYYYYN +NNNNNYYNN +YNYNYNYNN +2 2 +YN +NN +3 3 +YNY +NNN +NNY +25 7 +NYNNYNN +NNNNNNN +NNYNYYY +YNYNNNN +NNNYNNN +NYNNNYY +YYNNNNN +YYYNNNN +YNYNNYY +YNYYNYN +NYYYNNY +NNYNNNN +YYNYNNY +NNNNYYY +YNNNNNN +NYNNNNN +NNNYNYN +NNYNYNN +NYNNNNY +NYYNNNY +NYNNNYN +NNNNNNY +YNYYNNY +NNNNYNN +NNNYNNY +2 6 +NYYYYY +NNNYYY +2 9 +NYNYYYNYY +NNNNNNNNY +18 12 +NNNNNNNYNNNN +YNNNNNNNNNNN +NNNNNNYNNNNN +NNNNNNNNNNYN +NNNYYYNNNNNN +NNNNNNNNYNYN +NNNNNNNNNNNN +NNNYNNNNYNNY +NYNYNYNNNNYN +NYNNNNNNNNNN +YNNNYNNNNNNN +NNNNNNNNYNNN +YYYNNNNNNNNY +NNYYNYYNYNNN +NYNNNYNNNNNN +NNNYNNNNNNNN +NNNNNNYNYNYY +NYYNNNNNNNNN +2 5 +YYNYY +NNNYY +6 6 +NYNNNN +NNNYNN +YNYNNN +YNNNNN +YNYNYN +YNYYYN +2 11 +NYNYNNNYYYY +NNNYNNNYNYN +10 4 +NNYY +YNNN +NNNN +NNNY +YYNN +NYYN +YNYN +YYYN +NNYN +NYNN +7 9 +NNNNNNYNN +YNYNNNNYY +NYNNNYNYY +YNYNNYNNN +YNNNYYNNY +NYYNYYNNY +YNYNYYNYY +2 4 +YNNN +NNNN +2 12 +YYNYYYYNYNNN +NYNNYYYNNNNN +23 14 +NNNNNNYNNNNNNN +NYYNYNNNNNNNNN +NNYNNNNNNNNNYN +NNYNNNNNNNYNNN +NNYYYNNYNNNNNN +NYNNNNNYNNNNNN +NYYNNNNNNNNNNN +YYNNNNNYNNNYNN +NNNNNNNNNNNYYN +NNNNNNNNNNNNNY +YNYNNNNYNYNNNN +NYNYNNNNNNNNNN +NNNNNYNNNNNNNN +NNNNNNNNNNNYNN +NNNNNYNNNNNNYN +NNYNNNNNNNNNNN +NNNNNNNYNNNNNN +NNNNNNNNNYYYNN +NNNYYNNNNNYNYN +NNNNNNNNNNNNNN +YNNNNNNNNNNNNN +YNNNNYNYNNNNNY +NNYNYNNNNNNYYN +2 2 +NY +NN +8 5 +NYNYN +NNYNN +NNNYN +NYYNY +YYNNY +NYYNN +YYNNN +YYYNY +2 10 +NYYYYNYNYY +NYYYNNNNNY +400 400 +NYNNNYYYYYNYNNYNYYYYNYYYNNNYYYYNYYNNYNYYYNNYNNNNYYNYNYYNYYNNYNYYNNNYYNYYYYYYYYNNYYYYNNNYYYNNYYNNYYNNNNYNYNNNYYNNNNYYNYYNYYNNNNYNYNNYYNNYNYYNYNYYYYNYNYNYNYYYNNYYYYYNNYYNYNYYYNNNYYNNNYNYYYNYNNYYYYNNYNNYYYNYYYNNNYYYYYYNYNYNYYNYNNNYNYNNYYNNYNYYNYNYNYNNYYYNNYNNNYYYYNNYNYYYYNNNYYYNNNNNYNNYNNNYNNNNNYNNNNNNYNNYNNNNNYYNNNNNYNYNNNYYNNYYYNNNNYNYYNYYYYYYYNYNYNYYYYYNYNNNNYNYYNYYNYYYYYYYNYYNYYNNNYYNYYYYYYYNYNYY 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b/2019/finals/scoreboard.md new file mode 100644 index 0000000000000000000000000000000000000000..aabb014bff099057640237c33eb643bd1c92f64d --- /dev/null +++ b/2019/finals/scoreboard.md @@ -0,0 +1,61 @@ +The 2019 Hacker Cup Finals have just concluded! There were **N** participants +(numbered 1 to **N**), including yourself (competing as participant 1), and +**M** problems (numbered 1 to **M**). + +Participant _i_ solved problem _j_ if **Si,j** = "Y", and otherwise they +didn't solve it (if **Si,j** = "N"). Problem _i_'s point value is 2i, and each +participant's score is the sum of the point values of the problems that they +solved. No two participants solved exactly the same set of problems, which +also means that all participants have distinct scores. + +Before the final results get announced, you have an opportunity to rearrange +the **M** columns of the scoreboard **S** into any permutation of problems 1 +to **M**. For example, if you swap columns 1 and 2, then everybody who had +originally solved problem 1 will now be considered to have solved problem 2 +(thus earning 4 points for it rather than 2), and vice versa. + +Of course, you'd like to use this opportunity to your benefit — it would be +irresponsible to just let it pass by! However, it would be too suspicious if +you simply made yourself win the whole competition. As such, you'd like to +cause yourself to end up in 2nd place, such that you (participant 1) have +exactly the second-highest score out of all **N** participants. Now you just +need to determine whether or not this is achievable... + +### Input + +Input begins with an integer **T**, the number of scoreboards. +For each scoreboard, there is first a line containing the space-separated +integers **N** and **M**. +Then, **N** lines follow, the _i_th of which contains a length-**M** string, +the characters **Si,1** through **Si,M**. + +### Output + +For the _i_th scoreboard, print a line containing "Case #_i_: " followed by +one character, either "Y" if you can end up in 2nd place, or "N" otherwise. + +### Constraints + +1 ≤ **T** ≤ 200 +2 ≤ **N** ≤ 400 +1 ≤ **M** ≤ 400 + +The sum of **N** * **M** across all **T** test cases is no greater than +1,000,000. + +### Explanation of Sample + +In the first case, there's only one possible permutation of problems: [1]. +This results in you having a score of 2 and participant 2 having a score of 0, +which puts you in 1st place rather than 2nd. + +In the second case, if you preserve the original permutation of problems, [1, +2], you'll have a score of 2 while participant 2 has a score of 4, putting you +in 2nd place, as required. The permutation [2, 1] would have put you in 1st +place instead. + +In the third case, if you choose the problem permutation [2, 1], the 4 +participants' scores will be 4, 0, 6, and 2, respectively. This puts you in +2nd place, as required. The problem permutation [1, 2] would have put you in +3rd place instead. + diff --git a/2019/finals/scoreboard.out b/2019/finals/scoreboard.out new file mode 100644 index 0000000000000000000000000000000000000000..01a20a952dc485b7fbc5ffaf49b69127a5bd797d --- /dev/null +++ b/2019/finals/scoreboard.out @@ -0,0 +1,228 @@ +Case #1: N +Case #2: Y +Case #3: Y +Case #4: N +Case #5: Y +Case #6: N +Case #7: Y +Case #8: Y +Case #9: N +Case #10: N +Case #11: N +Case #12: N +Case #13: N +Case #14: N +Case #15: N +Case #16: N +Case #17: N +Case #18: N +Case #19: N +Case #20: N +Case #21: N +Case #22: N +Case #23: N +Case #24: N +Case #25: N +Case #26: N +Case #27: N +Case #28: N +Case #29: Y +Case #30: Y +Case #31: Y +Case #32: Y +Case #33: Y +Case #34: Y +Case #35: Y +Case #36: Y +Case #37: Y +Case #38: N +Case #39: N +Case #40: Y +Case #41: Y +Case #42: Y +Case #43: Y +Case #44: Y +Case #45: N +Case #46: Y +Case #47: N +Case #48: Y +Case #49: Y +Case #50: N +Case #51: N +Case #52: Y +Case #53: Y +Case #54: Y +Case #55: Y +Case #56: Y +Case #57: Y +Case #58: Y +Case #59: N +Case #60: Y +Case #61: Y +Case #62: Y +Case #63: Y +Case #64: Y +Case #65: Y +Case #66: Y +Case #67: Y +Case #68: Y +Case #69: Y +Case #70: Y +Case #71: Y +Case #72: Y +Case #73: Y +Case #74: Y +Case #75: Y +Case #76: Y +Case #77: Y +Case #78: Y +Case #79: Y +Case #80: N +Case #81: Y +Case #82: Y +Case #83: N +Case #84: Y +Case #85: Y +Case #86: Y +Case #87: Y +Case #88: Y +Case #89: Y +Case #90: Y +Case #91: Y +Case #92: Y +Case #93: Y +Case #94: Y +Case #95: Y +Case #96: Y +Case #97: Y +Case #98: Y +Case #99: Y +Case #100: Y +Case #101: N +Case #102: Y +Case #103: Y +Case #104: Y +Case #105: Y +Case #106: Y +Case #107: Y +Case #108: Y +Case #109: Y +Case #110: Y +Case #111: Y +Case #112: Y +Case #113: Y +Case #114: Y +Case #115: Y +Case #116: Y +Case #117: N +Case #118: Y +Case #119: Y +Case #120: Y +Case #121: Y +Case #122: Y +Case #123: Y +Case #124: Y +Case #125: Y +Case #126: Y +Case #127: Y +Case #128: Y +Case #129: Y +Case #130: Y +Case #131: Y +Case #132: Y +Case #133: Y +Case #134: Y +Case #135: Y +Case #136: Y +Case #137: N +Case #138: N +Case #139: Y +Case #140: Y +Case #141: N +Case #142: Y +Case #143: Y +Case #144: Y +Case #145: Y +Case #146: Y +Case #147: N +Case #148: Y +Case #149: Y +Case #150: Y +Case #151: Y +Case #152: Y +Case #153: Y +Case #154: Y +Case #155: Y +Case #156: Y +Case #157: Y +Case #158: Y +Case #159: Y +Case #160: Y +Case #161: N +Case #162: Y +Case #163: Y +Case #164: Y +Case #165: Y +Case #166: Y +Case #167: N +Case #168: Y +Case #169: Y +Case #170: N +Case #171: Y +Case #172: Y +Case #173: Y +Case #174: Y +Case #175: Y +Case #176: Y +Case #177: Y +Case #178: Y +Case #179: Y +Case #180: Y +Case #181: N +Case #182: Y +Case #183: Y +Case #184: Y +Case #185: Y +Case #186: Y +Case #187: Y +Case #188: N +Case #189: Y +Case #190: Y +Case #191: Y +Case #192: Y +Case #193: Y +Case #194: N +Case #195: Y +Case #196: Y +Case #197: Y +Case #198: Y +Case #199: Y +Case #200: Y +Case #201: Y +Case #202: Y +Case #203: Y +Case #204: N +Case #205: Y +Case #206: Y +Case #207: Y +Case #208: Y +Case #209: Y +Case #210: N +Case #211: Y +Case #212: Y +Case #213: Y +Case #214: Y +Case #215: Y +Case #216: Y +Case #217: Y +Case #218: N +Case #219: Y +Case #220: Y +Case #221: N +Case #222: Y +Case #223: Y +Case #224: Y +Case #225: Y +Case #226: Y +Case #227: Y +Case #228: Y diff --git a/2019/finals/strings_as_a_service.html b/2019/finals/strings_as_a_service.html new file mode 100644 index 0000000000000000000000000000000000000000..ca98bcef79db905f74487e772469fc75deaa0154 --- /dev/null +++ b/2019/finals/strings_as_a_service.html @@ -0,0 +1,90 @@ +

+Carlos has been working in technology so long that he's starting to feel a bit +burnt out. Hoping to rejuvenate himself, Carlos has been seeking out more +artistic opportunities. +

+ +

+Yamaha, the well-known creator of musical apparatus, has approached Carlos with +a request that might be right up his alley: they'd like him to design a brand new +instrument. Immediately, Carlos knows what to do. +

+ +

+"You may have seen Pat Metheny's 42-string guitar, but that's nothing compared +to what we're going to make together." +

+ +

+Carlos presents his plan for a 1,000-string guitar, complete with programmatic +tuning so that you don't need to turn 1,000 knobs by hand. Yamaha's market +research suggests that these sorts of guitars would be great for playing +palindromic chords, chords where the first string plays the same note as the +last string, the second string plays the same note as the second-to-last +string, and so on. Carlos is quickly tasked with developing default tunings for +the strings so that the guitars are ready to play right out of the box. +

+ +

+For various integers K, Carlos wants to find a set of at most 1,000 strings on which +exactly K distinct palindromic chords can be played. The guitar's strings are +arranged in a line, and each one must be tuned to a note from the set {A, B, C, D, E, F, G}. +A chord is then played by strumming a contiguous subset of +1 or more strings. Two chords are considered to be distinct if there is at least one +string that is used in one chord but not the other; chords involving the same notes but +different strings are considered different. +

+ +

+For example, if K = 9, a set of 7 strings could be tuned to the notes +C, A, B, B, A, G, E in order from left to right. You can play 7 different palindromic +chords by strumming single strings, the chord BB by strumming the 3rd and 4th +strings, and the chord ABBA by strumming the 2nd, 3rd, 4th, and 5th strings. +This is a total of 9 distinct palindromic chords. + + +

+Output any non-empty string of valid musical notes, with length at most 1,000, +representing the tunings of sequential strings. An aspiring musician must be able +to play exactly K distinct palindromic chords on these strings. It's guaranteed +that there is at least one valid output for each possible valid input. +

+ + +

Input

+ +

+Input begins with an integer T, the number of tunings that Carlos needs to figure out. +
For each tuning, there is a single line containing the integer K. +

+ + +

Output

+ +

+For the ith tuning, print a line containing "Case #i: " followed by a string of up to 1,000 characters representing +a tuning of strings as described above on which exactly K distinct palindromic chords can be played. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 500
+1 ≤ K ≤ 100,000
+

+ +

Explanation of Sample

+ +

+In the first case, "ACE" is a valid output as it contains exactly 3 palindromes: "A", "C", and "E". On the other hand, "DAD" would not be valid as it contains 4 palindromes. +

+ +

+In the second case, "GAGA" is a valid output as it contains exactly 6 palindromes: "G", "A", "G", "A", "GAG", and "AGA". +

+ +

+Note that other outputs would also be accepted for each sample case. +

+ diff --git a/2019/finals/strings_as_a_service.in b/2019/finals/strings_as_a_service.in new file mode 100644 index 0000000000000000000000000000000000000000..6e1e6f2613c66bcb95d61a8c7e09b39ba581a81a --- /dev/null +++ b/2019/finals/strings_as_a_service.in @@ -0,0 +1,506 @@ +505 +3 +6 +7 +9 +16 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +15 +16 +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38 +39 +40 +41 +42 +43 +44 +45 +46 +47 +48 +49 +50 +51 +52 +53 +54 +55 +56 +57 +58 +59 +60 +61 +62 +63 +64 +65 +66 +67 +68 +69 +70 +71 +72 +73 +74 +75 +76 +77 +78 +79 +80 +81 +82 +83 +84 +85 +86 +87 +88 +89 +90 +91 +92 +93 +94 +95 +96 +97 +98 +99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 +148 +149 +150 +100000 +99999 +99998 +99997 +99996 +99995 +99994 +99993 +99992 +99991 +99990 +99989 +99988 +99987 +99986 +99985 +99984 +99983 +99982 +99981 +99980 +99979 +99978 +99977 +99976 +99975 +99974 +99973 +99972 +99971 +99970 +99969 +99968 +99967 +99966 +99965 +99964 +99963 +99962 +99961 +99960 +99959 +99958 +99957 +99956 +99955 +99954 +99953 +99952 +99951 +99950 +99949 +99948 +99947 +99946 +99945 +99944 +99943 +99942 +99941 +99940 +99939 +99938 +99937 +99936 +99935 +99934 +99933 +99932 +99931 +99930 +99929 +99928 +99927 +99926 +99925 +99924 +99923 +99922 +99921 +99920 +99919 +99918 +99917 +99916 +99915 +99914 +99913 +99912 +99911 +99910 +99909 +99908 +99907 +99906 +99905 +99904 +99903 +99902 +99901 +99900 +99899 +99898 +99897 +99896 +99895 +99894 +99893 +99892 +99891 +99890 +99889 +99888 +99887 +99886 +99885 +99884 +99883 +99882 +99881 +99880 +99879 +99878 +99877 +99876 +99875 +99874 +99873 +99872 +99871 +99870 +99869 +99868 +99867 +99866 +99865 +99864 +99863 +99862 +99861 +99860 +99859 +99858 +99857 +99856 +99855 +99854 +99853 +99852 +99851 +28292 +26487 +28200 +75718 +94504 +30221 +8344 +2567 +41769 +75836 +64842 +48960 +82375 +42091 +15523 +54684 +68127 +11839 +65064 +36442 +20124 +63038 +31982 +22342 +3268 +63593 +26154 +9236 +16207 +22653 +70167 +37104 +15290 +86487 +92629 +29708 +54514 +64705 +30662 +66503 +1076 +74062 +50093 +79615 +37386 +13477 +95000 +4763 +33135 +12117 +34444 +50559 +64851 +83630 +73471 +57916 +25954 +7967 +49576 +77323 +56182 +47882 +90202 +79294 +53005 +53024 +91112 +12044 +21038 +4362 +80235 +26247 +54621 +46429 +48015 +33044 +11542 +21169 +83396 +5350 +57358 +16743 +59631 +95143 +5940 +2804 +20832 +90284 +74343 +78958 +10223 +45771 +41425 +86449 +18344 +51140 +74113 +60207 +9693 +36377 +15007 +13738 +74283 +36019 +86696 +65239 +78052 +66819 +4361 +43905 +91051 +8442 +74736 +49871 +93999 +30022 +18061 +16779 +11975 +16921 +35656 +49216 +6283 +21215 +10733 +63655 +38835 +71036 +35034 +66822 +89009 +26007 +52177 +56558 +10033 +71183 +9384 +30847 +17689 +27505 +23118 +97162 +15515 +19323 +87520 +13179 +43703 +21552 +98425 +31824 +60805 +46448 +31905 +34587 +57441 +3460 +30684 +12944 +83895 +26859 +92019 +12411 +74142 +85899 +36584 +88401 +43409 +10207 +43386 +50033 +95136 +13289 +26425 +3304 +27965 +36461 +40515 +68645 +72034 +11434 +38357 +7383 +3048 +36374 +30077 +43481 +52371 +34492 +93652 +68951 +48233 +53821 +23593 +66633 +76225 +17336 +28737 +89561 +48248 +68823 diff --git a/2019/finals/strings_as_a_service.md b/2019/finals/strings_as_a_service.md new file mode 100644 index 0000000000000000000000000000000000000000..d9f0d463b76ff78dca598487d594482b43067baf --- /dev/null +++ b/2019/finals/strings_as_a_service.md @@ -0,0 +1,68 @@ +Carlos has been working in technology so long that he's starting to feel a bit +burnt out. Hoping to rejuvenate himself, Carlos has been seeking out more +artistic opportunities. + +Yamaha, the well-known creator of musical apparatus, has approached Carlos +with a request that might be right up his alley: they'd like him to design a +brand new instrument. Immediately, Carlos knows what to do. + +_ "You may have seen Pat Metheny's 42-string guitar, but that's nothing +compared to what we're going to make together." _ + +Carlos presents his plan for a 1,000-string guitar, complete with programmatic +tuning so that you don't need to turn 1,000 knobs by hand. Yamaha's market +research suggests that these sorts of guitars would be great for playing +palindromic chords, chords where the first string plays the same note as the +last string, the second string plays the same note as the second-to-last +string, and so on. Carlos is quickly tasked with developing default tunings +for the strings so that the guitars are ready to play right out of the box. + +For various integers **K**, Carlos wants to find a set of at most 1,000 +strings on which exactly **K** distinct palindromic chords can be played. The +guitar's strings are arranged in a line, and each one must be tuned to a note +from the set {A, B, C, D, E, F, G}. A chord is then played by strumming a +contiguous subset of 1 or more strings. Two chords are considered to be +distinct if there is at least one string that is used in one chord but not the +other; chords involving the same notes but different strings are considered +different. + +For example, if **K** = 9, a set of 7 strings could be tuned to the notes C, +A, B, B, A, G, E in order from left to right. You can play 7 different +palindromic chords by strumming single strings, the chord BB by strumming the +3rd and 4th strings, and the chord ABBA by strumming the 2nd, 3rd, 4th, and +5th strings. This is a total of 9 distinct palindromic chords. ** + +Output any non-empty string of valid musical notes, with length at most 1,000, +representing the tunings of sequential strings. An aspiring musician must be +able to play exactly **K** distinct palindromic chords on these strings. It's +guaranteed that there is at least one valid output for each possible valid +input. + +### Input + +Input begins with an integer **T**, the number of tunings that Carlos needs to +figure out. +For each tuning, there is a single line containing the integer **K**. + +### Output + +For the _i_th tuning, print a line containing "Case #_i_: " followed by a +string of up to 1,000 characters representing a tuning of strings as described +above on which exactly **K** distinct palindromic chords can be played. + +### Constraints + +1 ≤ **T** ≤ 500 +1 ≤ **K** ≤ 100,000 + +### Explanation of Sample + +In the first case, "ACE" is a valid output as it contains exactly 3 +palindromes: "A", "C", and "E". On the other hand, "DAD" would not be valid as +it contains 4 palindromes. + +In the second case, "GAGA" is a valid output as it contains exactly 6 +palindromes: "G", "A", "G", "A", "GAG", and "AGA". + +**_Note that other outputs would also be accepted for each sample case._** + diff --git a/2019/finals/strings_as_a_service.out b/2019/finals/strings_as_a_service.out new file mode 100644 index 0000000000000000000000000000000000000000..b140b30a91174e797b5aa3be2b3f3e1dab8454ba --- /dev/null +++ b/2019/finals/strings_as_a_service.out @@ -0,0 +1,505 @@ +Case #1: AA +Case #2: AAA +Case #3: AAAB +Case #4: AAABB +Case #5: AAAAAB +Case #6: A +Case #7: AB +Case #8: AA +Case #9: AAB +Case #10: AABC +Case #11: AAA +Case #12: AAAB +Case #13: AAABC +Case #14: AAABB +Case #15: AAAA +Case #16: AAAAB +Case #17: AAAABC +Case #18: AAAABB +Case #19: AAAABBC +Case #20: AAAAA +Case #21: AAAAAB +Case #22: AAAAABC +Case #23: AAAAABB +Case #24: AAAAABBC +Case #25: AAAAABBCA +Case #26: AAAAAA +Case #27: AAAAAAB 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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCCAAB +Case #181: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCCAA +Case #182: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCCAB +Case #183: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCCA +Case #184: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCC +Case #185: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCAAB +Case #186: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCAA +Case #187: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCAB +Case #188: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCA +Case #189: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCC +Case #190: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCAA +Case #191: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCAB +Case #192: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCA +Case #193: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCC +Case #194: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCAB +Case #195: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCA +Case #196: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCC +Case #197: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCA +Case #198: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBC +Case #199: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBB +Case #200: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCCCA +Case #201: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCCC +Case #202: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCCAABC +Case #203: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCCAAB +Case #204: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCCAA +Case #205: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCCAB +Case #206: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCCA +Case #207: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCC +Case #208: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCAAB +Case #209: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCAA +Case #210: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCAB +Case #211: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCA +Case #212: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCC +Case #213: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCAA +Case #214: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCAB +Case #215: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCA +Case #216: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCC +Case #217: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCAB +Case #218: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCA +Case #219: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCC +Case #220: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCA +Case #221: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBC +Case #222: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBB +Case #223: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCCC +Case #224: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCCAABC +Case #225: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCCAAB +Case #226: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCCAA +Case #227: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCCAB +Case #228: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCCA +Case #229: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCC +Case #230: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCAAB +Case #231: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCAA +Case #232: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCAB +Case #233: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCA +Case #234: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCC +Case #235: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCAA +Case #236: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCAB +Case #237: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCA +Case #238: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCC +Case #239: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCAB +Case #240: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCA +Case #241: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCC +Case #242: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCA +Case #243: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBC +Case #244: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBB +Case #245: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCCAABC +Case #246: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCCAAB +Case #247: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCCAA +Case #248: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCCAB +Case #249: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCCA +Case #250: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCC +Case #251: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCAAB +Case #252: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCAA +Case #253: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCAB +Case #254: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCA +Case #255: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCC +Case #256: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCAA +Case #257: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCAB +Case #258: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCA +Case #259: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCC +Case #260: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCAB +Case #261: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCA +Case #262: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCC +Case #263: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCA +Case #264: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBC +Case #265: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBB +Case #266: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCCCAAB +Case #267: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCCCAA +Case #268: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCCCAB +Case #269: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCCCA +Case #270: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCCC +Case #271: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCCAAB +Case #272: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCCAA +Case #273: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCCAB +Case #274: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCCA +Case #275: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCC +Case #276: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCAA +Case #277: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCAB +Case #278: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCA +Case #279: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCC +Case #280: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCAB +Case #281: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCA +Case #282: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCC +Case #283: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCA +Case #284: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBC +Case #285: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBB +Case #286: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCCAA +Case #287: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCCAB +Case #288: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCCA +Case #289: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCC +Case #290: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCAAB +Case #291: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCAA +Case #292: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCAB +Case #293: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCA +Case #294: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCC +Case #295: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCAA +Case #296: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCAB +Case #297: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCA +Case #298: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCC +Case #299: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCAB +Case #300: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCA +Case #301: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCC +Case #302: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCA +Case #303: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBC +Case #304: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBB +Case #305: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBCCCCCAB +Case #306: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCCCA +Case #307: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBCCCCCA +Case #308: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCC +Case #309: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCCC +Case #310: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBCCA +Case #311: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCCAB +Case #312: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCCC +Case #313: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBC +Case #314: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBB +Case #315: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCAAB +Case #316: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCAB +Case #317: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCCAB +Case #318: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBCCCA +Case #319: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCC +Case #320: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCC +Case #321: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBCC +Case #322: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBB +Case #323: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBCC +Case #324: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCC +Case #325: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCA +Case #326: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBCC +Case #327: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCCAA +Case #328: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBCCCCAA +Case #329: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCCA +Case #330: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBB +Case #331: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBCA +Case #332: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBCC +Case #333: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBC +Case #334: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBCCC +Case #335: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBCCCAA +Case #336: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBCCC +Case #337: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCCAB +Case #338: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBCCCC +Case #339: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBCCCCAAB +Case #340: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCA +Case #341: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBCCCA +Case #342: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCCAAB +Case #343: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCCA +Case #344: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBCCC +Case #345: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBCCCA +Case #346: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBCCAB +Case #347: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBCCC +Case #348: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBC +Case #349: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCA +Case #350: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCAB +Case #351: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBCCC +Case #352: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBCCCCCAB +Case #353: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBB +Case #354: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCAB +Case #355: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBCCC +Case #356: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBB +Case #357: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBCC +Case #358: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBB +Case #359: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCA +Case #360: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBCCCCCAA +Case #361: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCC +Case #362: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBCCCC +Case #363: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBC +Case #364: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBC +Case #365: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCCAAB +Case #366: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCC +Case #367: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCCAABC +Case #368: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBCCCCA +Case #369: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCC +Case #370: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBCA +Case #371: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBCCA +Case #372: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBCCCAB +Case #373: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBCCA +Case #374: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCAB +Case #375: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCC +Case #376: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBCCCA +Case #377: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBCCAB +Case #378: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBB +Case #379: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBCC +Case #380: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBB +Case #381: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBCCCCAB +Case #382: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBB +Case #383: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBCCCAA +Case #384: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCAB +Case #385: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBCCC +Case #386: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBC +Case #387: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCCCAB +Case #388: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCCCCC +Case #389: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBCCCCAA +Case #390: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBCCCAA +Case #391: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBC +Case #392: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCC +Case #393: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCAA +Case #394: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBCA +Case #395: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBC +Case #396: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBCCA +Case #397: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBCC +Case #398: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBCCC +Case #399: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCAA +Case #400: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBCA +Case #401: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBCCCAA +Case #402: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCC +Case #403: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCAB +Case #404: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBCCCCA +Case #405: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBCCCA +Case #406: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCAA +Case #407: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBCCCA +Case #408: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBCCCCAB +Case #409: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCC +Case #410: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCAAB +Case #411: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCC +Case #412: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCC +Case #413: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBCC +Case #414: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCAB +Case #415: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCCCAAB +Case #416: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBCCCAA +Case #417: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBCA +Case #418: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBB +Case #419: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBCCCC +Case #420: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBCA +Case #421: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCCAB +Case #422: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBC +Case #423: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCC +Case #424: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBCCA +Case #425: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCCA +Case #426: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBCCCAA +Case #427: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBCCCAA +Case #428: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBC +Case #429: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBCCCAA +Case #430: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABC +Case #431: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBCCA +Case #432: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBCCCAA +Case #433: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBCCCA +Case #434: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBCCCAA +Case #435: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBCCC +Case #436: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCA +Case #437: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCAA +Case #438: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCC +Case #439: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBCA +Case #440: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBC +Case #441: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBCCCA +Case #442: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBCA +Case #443: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCAA +Case #444: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBCCC +Case #445: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBB +Case #446: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBCCCAB +Case #447: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBCCC +Case #448: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBCCCC +Case #449: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBCA +Case #450: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCA +Case #451: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBCA +Case #452: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBCCCA +Case #453: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBCC +Case #454: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBC +Case #455: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCAB +Case #456: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBC +Case #457: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCCC +Case #458: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBCCC +Case #459: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCCAAB +Case #460: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBCCCCAAB +Case #461: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBCA +Case #462: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBC +Case #463: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBCCCAA +Case #464: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBCCAB +Case #465: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBCCCAB +Case #466: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCC +Case #467: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBCA +Case #468: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBCCCCAB +Case #469: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBBCA +Case #470: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCCCA +Case #471: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBBCCAB +Case #472: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBCCCAB +Case #473: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBCCCAA +Case #474: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBB +Case #475: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBCCCC +Case #476: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBCCC +Case #477: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCCAB +Case #478: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCCCAB +Case #479: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBCCCAA +Case #480: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBCCA +Case #481: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBCCCC +Case #482: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBB +Case #483: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBB +Case #484: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBCC +Case #485: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBCCA +Case #486: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCCA +Case #487: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABC +Case #488: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBB +Case #489: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBCCA +Case #490: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCCA +Case #491: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBCCCCA +Case #492: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBB +Case #493: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBCC +Case #494: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCA +Case #495: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBCCCCCA +Case #496: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBB +Case #497: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCC +Case #498: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBCCA +Case #499: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBCCCCAA +Case #500: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCAAB +Case #501: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCCA +Case #502: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBCA +Case #503: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBCCCAB +Case #504: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBCCCA +Case #505: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCCCAB diff --git a/2019/finals/temporal_revision.html b/2019/finals/temporal_revision.html new file mode 100644 index 0000000000000000000000000000000000000000..9688b28f17d256b56484ea3db30ecb3eaccee18c --- /dev/null +++ b/2019/finals/temporal_revision.html @@ -0,0 +1,176 @@ +

+The starship Enterprise, bravely captained by Jean-Luc Picard, is on yet another mission to explore strange new worlds, seek out new life and new civilizations, +and boldly go where no one has gone before! Equipped with a state-of-the-art warp drive capable of attaining warp factor 11 and revising the Enterprise's space-time coordinates almost at will +(even sending the ship back in time), not much can stand in the explorers' way. Though, they are low on medical supplies, so they will need to first stock up on neurozine gas for anesthetic purposes. +

+ +

+The Enterprise is heading to the Alpha Omicron solar system, which consists of N planets, numbered from 1 to N. +It also features M space conduits, the ith of which allows the Enterprise to travel in either direction between two different planets +Ai and Bi. +No two conduits directly link the same unordered pair of planets, and each planet is reachable from each other planet by following a sequence of conduits. +

+ +

+There's a geyser capable of emitting neurozine located on each planet, though all N geysers are initially inactive. +A sequence of K events will then take place, one per hour. The event at hour i is described by integers Ei and Vi, +with Ei indicating the event's type, which is one of the following: +

+ +
    +
  • Ei = 1: The Vith conduit (1 ≤ ViM) collapses, +and can no longer be used from that moment onwards. Each conduit collapses at most once.
  • +
  • Ei = 2: The geyser on planet Vi (1 ≤ ViN) activates, +and begins emitting neurozine. Each geyser is activated at most once.
  • +
  • Ei = 3: The geyser on planet Vi (1 ≤ ViN) deactivates, +and no longer emits neurozine from that moment onwards. Each geyser is deactivated at most once, and is guaranteed to not be deactivated before it has been activated.
  • +
+ +

+The Enterprise will arrive in the Alpha Omicron system at some planet x and just before some hour y. +When the starship is currently at a certain planet (and a certain time), Captain Picard may issue any of the following commands to his crew: +

+ +
    +
  • Remain at that planet and wait until any future time.
  • +
  • Travel through an uncollapsed space conduit directly from that planet to another one. Thanks to warp technology, this may be done instantly.
  • +
  • Collect neurozine from that planet's geyser, if it's currently active. This may be done instantly.
  • +
  • Remain at that planet while travelling backwards to any past time which is at most 24 hours earlier than the Enterprise's original arrival time in the solar system +(in other words, the Enterprise may end up just before hour (y - 24), but no earlier). However, this may only be done at most once. The Enterprise retains any neurozine that it had collected before this "temporal revision". +
+ +

+Picard wants his crew to collect neurozine from as many different geysers as possible; there's no additional value in collecting neurozine from any given geyser multiple times, +including both before and after travelling back in time. However, Picard hasn't yet decided where and when the Enterprise should arrive in the Alpha Omicron system. +He has S such possible starting situations in mind, the ith of which would have the Enterprise arrive at planet +Xi just before hour Yi. +For each hypothetical starting situation, please help Picard determine the maximum number of different geysers from which the Enterprise could then proceed to collect neurozine! +

+ +

+Letting ansi be the answer for the ith starting situation, you must output the sum of ans1..S +in order to minimize the size of the output. Please note that this sum may not fit within a 32-bit integer. +

+ +

+The starting situations must be considered one after another. In order to enforce this, rather than being given X1..S and Y1..S +explicitly, you must compute them based on given values X'1..S and Y'1..S. +For the first starting situation, X1 = X'1 and Y1 = Y'1, +while for each subsequent starting situation i (2 ≤ iS), +Xi = X'i xor ansi-1 and +Yi = Y'i xor ansi-1 (where "xor" is the bitwise xor operator, "^" in most programming languages). +

+ + +

Input

+ +

+Input begins with an integer T, the number of missions. +
For each mission, there is first a line containing the space-separated integers N, M, K and S. +
Then, M lines follow, the ith of which contains the space-separated integers Ai and Bi. +
Then, K lines follow, the ith of which contains the space-separated integers Ei and Vi. +
Then, S lines follow, the ith of which contains the space-separated integers X'i and Y'i. +

+ + +

Output

+ +

+For the ith mission, print a line containing "Case #i: " followed by +one integer, the sum of the answers for the S starting situations. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 100
+2 ≤ N ≤ 800,000
+1 ≤ M, K, S ≤ 800,000
+1 ≤ Ai, BiN
+1 ≤ Ei ≤ 3
+1 ≤ XiN
+1 ≤ YiK
+0 ≤ X'i, Y'i ≤ 1,000,000,000
+

+ +

+The sum of N across all T test cases is no greater than 2,000,000.
+The sum of M across all T test cases is no greater than 2,000,000.
+The sum of K across all T test cases is no greater than 2,000,000.
+The sum of S across all T test cases is no greater than 2,000,000. +

+ + +

Explanation of Sample

+ +

+In the first case, if the Enterprise arrives at planet 1 just before hour 3, Picard could issue the following sequence of orders to help his crew collect neurozine from both planets' geysers: + +

    +
  1. Travel through the 1st space conduit to planet 2. +
  2. Wait until after hour 3. +
  3. Collect neurozine from planet 2's now-active geyser. +
  4. Travel back in time to just before hour 2. +
  5. Travel through the 1st space conduit to planet 1. +
  6. Collected neurozine from planet 1's active geyser. +
+ +

+In the second case, the starting situations and corresponding answers are as follows: +

+ +
+  i | Xi | Yi | ansi
+  ------------------
+  1 |  2 |  1 |    3
+  2 |  1 |  6 |    2
+  3 |  3 |  5 |    3
+
+ +

+For the first starting situation, the Enterprise could remain on planet 2 until its geyser activates at hour 6, collect its neurozine, travel back in time to just before hour 2, travel to planet 1 and collect its neurozine, travel to planet 2 and then to planet 3, and remain there to collect its neurozine after hour 5. On the other hand, for the second starting situation, neurozine from all 3 geysers cannot be collected. +

+ +

+In the third case, the starting situations and corresponding answers are as follows: +

+ +
+  i | Xi | Yi | ansi
+  ------------------
+  1 |  1 |  4 |    4
+  2 |  5 |  8 |    3
+  3 |  2 |  9 |    3
+  4 |  3 |  6 |    4
+
+ +

+In the fourth case, the starting situations and corresponding answers are as follows: +

+ +
+  i | Xi | Yi | ansi
+  ------------------
+  1 |  6 | 16 |    7
+  2 |  4 |  6 |    8
+  3 | 10 | 22 |    7
+  4 |  3 | 13 |    7
+  5 |  6 | 11 |    8
+  6 |  5 | 17 |    6
+  7 |  2 | 21 |    7
+
+ +

+In the fifth case, the first 5 starting situations and corresponding answers are as follows: +

+ +
+  i | Xi | Yi | ansi
+  ------------------
+  1 | 20 | 47 |    2
+  2 |  4 | 49 |    7
+  3 | 24 | 47 |    1
+  4 | 20 |  9 |   13
+  5 |  3 | 38 |    9
+
diff --git a/2019/finals/temporal_revision.in b/2019/finals/temporal_revision.in new file mode 100644 index 0000000000000000000000000000000000000000..cecbe1db83fb5dc9c8f179075b154c106b9f1099 --- /dev/null +++ b/2019/finals/temporal_revision.in @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:aa70fab4188368dde6802bbfdd1a06688cdf19812c546421ac0fe2b3c94d79e7 +size 58317500 diff --git a/2019/finals/temporal_revision.md b/2019/finals/temporal_revision.md new file mode 100644 index 0000000000000000000000000000000000000000..408c4e7d5df2028716cfefc3e38b278bb4afb183 --- /dev/null +++ b/2019/finals/temporal_revision.md @@ -0,0 +1,154 @@ +The starship Enterprise, bravely captained by Jean-Luc Picard, is on yet +another mission to explore strange new worlds, seek out new life and new +civilizations, and boldly go where no one has gone before! Equipped with a +state-of-the-art warp drive capable of attaining warp factor 11 and revising +the Enterprise's space-time coordinates almost at will (even sending the ship +back in time), not much can stand in the explorers' way. Though, they _are_ +low on medical supplies, so they will need to first stock up on neurozine gas +for anesthetic purposes. + +The Enterprise is heading to the Alpha Omicron solar system, which consists of +**N** planets, numbered from 1 to **N**. It also features **M** space +conduits, the _i_th of which allows the Enterprise to travel in either +direction between two different planets **Ai** and **Bi**. No two conduits +directly link the same unordered pair of planets, and **each planet is +reachable from each other planet** by following a sequence of conduits. + +There's a geyser capable of emitting neurozine located on each planet, though +all **N** geysers are initially inactive. A sequence of **K** events will then +take place, one per hour. The event at hour _i_ is described by integers +**Ei** and **Vi**, with **Ei** indicating the event's type, which is one of +the following: + + * **Ei** = 1: The **Vi**th conduit (1 ≤ **Vi** ≤ **M**) collapses, and can no longer be used from that moment onwards. Each conduit collapses at most once. + * **Ei** = 2: The geyser on planet **Vi** (1 ≤ **Vi** ≤ **N**) activates, and begins emitting neurozine. Each geyser is activated at most once. + * **Ei** = 3: The geyser on planet **Vi** (1 ≤ **Vi** ≤ **N**) deactivates, and no longer emits neurozine from that moment onwards. Each geyser is deactivated at most once, and is guaranteed to not be deactivated before it has been activated. + +The Enterprise will arrive in the Alpha Omicron system at some planet _x_ and +just before some hour _y_. When the starship is currently at a certain planet +(and a certain time), Captain Picard may issue any of the following commands +to his crew: + + * Remain at that planet and wait until any future time. + * Travel through an uncollapsed space conduit directly from that planet to another one. Thanks to warp technology, this may be done instantly. + * Collect neurozine from that planet's geyser, if it's currently active. This may be done instantly. + * Remain at that planet while travelling backwards to any past time which is **at most 24 hours earlier than the Enterprise's original arrival time in the solar system** (in other words, the Enterprise may end up just before hour (_y_ \- 24), but no earlier). However, **this may only be done at most once**. The Enterprise retains any neurozine that it had collected before this "temporal revision". + +Picard wants his crew to collect neurozine from as many _different_ geysers as +possible; there's no additional value in collecting neurozine from any given +geyser multiple times, including both before and after travelling back in +time. However, Picard hasn't yet decided where and when the Enterprise should +arrive in the Alpha Omicron system. He has **S** such possible starting +situations in mind, the _i_th of which would have the Enterprise arrive at +planet **Xi** just before hour **Yi**. For each hypothetical starting +situation, please help Picard determine the maximum number of different +geysers from which the Enterprise could then proceed to collect neurozine! + +Letting **ansi** be the answer for the _i_th starting situation, you must +output the sum of **ans1..S** in order to minimize the size of the output. +Please note that this sum may not fit within a 32-bit integer. + +The starting situations must be considered one after another. In order to +enforce this, rather than being given **X1..S** and **Y1..S** explicitly, you +must compute them based on given values **X'1..S** and **Y'1..S**. For the +first starting situation, **X1** = **X'1** and **Y1** = **Y'1**, while for +each subsequent starting situation _i_ (2 ≤ _i_ ≤ **S**), **Xi** = **X'i** xor +**ansi-1** and **Yi** = **Y'i** xor **ansi-1** (where "xor" is the bitwise xor +operator, "^" in most programming languages). + +### Input + +Input begins with an integer **T**, the number of missions. +For each mission, there is first a line containing the space-separated +integers **N**, **M**, **K** and **S**. +Then, **M** lines follow, the _i_th of which contains the space-separated +integers **Ai** and **Bi**. +Then, **K** lines follow, the _i_th of which contains the space-separated +integers **Ei** and **Vi**. +Then, **S** lines follow, the _i_th of which contains the space-separated +integers **X'i** and **Y'i**. + +### Output + +For the _i_th mission, print a line containing "Case #_i_: " followed by one +integer, the sum of the answers for the **S** starting situations. + +### Constraints + +1 ≤ **T** ≤ 100 +2 ≤ **N** ≤ 800,000 +1 ≤ **M**, **K**, **S** ≤ 800,000 +1 ≤ **Ai**, **Bi** ≤ **N** +1 ≤ **Ei** ≤ 3 +1 ≤ **Xi** ≤ **N** +1 ≤ **Yi** ≤ **K** +0 ≤ **X'i**, **Y'i** ≤ 1,000,000,000 + +The sum of **N** across all **T** test cases is no greater than 2,000,000. +The sum of **M** across all **T** test cases is no greater than 2,000,000. +The sum of **K** across all **T** test cases is no greater than 2,000,000. +The sum of **S** across all **T** test cases is no greater than 2,000,000. + +### Explanation of Sample + +In the first case, if the Enterprise arrives at planet 1 just before hour 3, +Picard could issue the following sequence of orders to help his crew collect +neurozine from both planets' geysers: + + 1. Travel through the 1st space conduit to planet 2. + 2. Wait until after hour 3. + 3. Collect neurozine from planet 2's now-active geyser. + 4. Travel back in time to just before hour 2. + 5. Travel through the 1st space conduit to planet 1. + 6. Collected neurozine from planet 1's active geyser. + +In the second case, the starting situations and corresponding answers are as +follows: + + i | Xi | Yi | ansi + ------------------ + 1 | 2 | 1 | 3 + 2 | 1 | 6 | 2 + 3 | 3 | 5 | 3 + +For the first starting situation, the Enterprise could remain on planet 2 +until its geyser activates at hour 6, collect its neurozine, travel back in +time to just before hour 2, travel to planet 1 and collect its neurozine, +travel to planet 2 and then to planet 3, and remain there to collect its +neurozine after hour 5. On the other hand, for the second starting situation, +neurozine from all 3 geysers cannot be collected. + +In the third case, the starting situations and corresponding answers are as +follows: + + i | Xi | Yi | ansi + ------------------ + 1 | 1 | 4 | 4 + 2 | 5 | 8 | 3 + 3 | 2 | 9 | 3 + 4 | 3 | 6 | 4 + +In the fourth case, the starting situations and corresponding answers are as +follows: + + i | Xi | Yi | ansi + ------------------ + 1 | 6 | 16 | 7 + 2 | 4 | 6 | 8 + 3 | 10 | 22 | 7 + 4 | 3 | 13 | 7 + 5 | 6 | 11 | 8 + 6 | 5 | 17 | 6 + 7 | 2 | 21 | 7 + +In the fifth case, the first 5 starting situations and corresponding answers +are as follows: + + i | Xi | Yi | ansi + ------------------ + 1 | 20 | 47 | 2 + 2 | 4 | 49 | 7 + 3 | 24 | 47 | 1 + 4 | 20 | 9 | 13 + 5 | 3 | 38 | 9 + diff --git a/2019/finals/temporal_revision.out b/2019/finals/temporal_revision.out new file mode 100644 index 0000000000000000000000000000000000000000..697497d3d3ab0fc20aed535ca3ca2e92dbadfe58 --- /dev/null +++ b/2019/finals/temporal_revision.out @@ -0,0 +1,105 @@ +Case #1: 2 +Case #2: 8 +Case #3: 14 +Case #4: 50 +Case #5: 246 +Case #6: 62566449144 +Case #7: 160070740347 +Case #8: 1090 +Case #9: 2067 +Case #10: 768 +Case #11: 4601 +Case #12: 1795 +Case #13: 721 +Case #14: 2167 +Case #15: 3033 +Case #16: 3658 +Case #17: 499 +Case #18: 1197 +Case #19: 3693 +Case #20: 5085 +Case #21: 613 +Case #22: 3581 +Case #23: 724 +Case #24: 1036 +Case #25: 6595 +Case #26: 0 +Case #27: 527 +Case #28: 908 +Case #29: 766 +Case #30: 2603 +Case #31: 1342 +Case #32: 360 +Case #33: 824 +Case #34: 1751 +Case #35: 2598 +Case #36: 2603 +Case #37: 3399 +Case #38: 419 +Case #39: 3818 +Case #40: 354 +Case #41: 365 +Case #42: 990 +Case #43: 2042 +Case #44: 6166 +Case #45: 856 +Case #46: 2922 +Case #47: 575 +Case #48: 3600 +Case #49: 368 +Case #50: 1924 +Case #51: 2920 +Case #52: 1612 +Case #53: 2536 +Case #54: 3212 +Case #55: 913 +Case #56: 5088 +Case #57: 1161 +Case #58: 3514 +Case #59: 844 +Case #60: 2037 +Case #61: 997 +Case #62: 1464 +Case #63: 84 +Case #64: 2134 +Case #65: 1608 +Case #66: 1837 +Case #67: 1992 +Case #68: 3517 +Case #69: 1279 +Case #70: 1547 +Case #71: 1030 +Case #72: 1089 +Case #73: 87 +Case #74: 379 +Case #75: 1811 +Case #76: 1728 +Case #77: 570 +Case #78: 528 +Case #79: 1698 +Case #80: 5504 +Case #81: 3123 +Case #82: 124 +Case #83: 2190 +Case #84: 3993 +Case #85: 85 +Case #86: 870 +Case #87: 335 +Case #88: 1538 +Case #89: 450 +Case #90: 2524 +Case #91: 3776 +Case #92: 3947 +Case #93: 1978 +Case #94: 632 +Case #95: 1298 +Case #96: 2336 +Case #97: 2945 +Case #98: 2075 +Case #99: 2215 +Case #100: 1742 +Case #101: 3161 +Case #102: 1258 +Case #103: 2993 +Case #104: 2086 +Case #105: 2449 diff --git a/2019/quals/leapfrog1.cpp b/2019/quals/leapfrog1.cpp new file mode 100644 index 0000000000000000000000000000000000000000..5a4303e2d41de4be2b9353f4ae01b364af08e61e --- /dev/null +++ b/2019/quals/leapfrog1.cpp @@ -0,0 +1,112 @@ +// Leapfrog Ch. 1 +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int N; + int i,c; + char S[5005]; + // testcase loop + Read(T); + Fox1(t,T) + { + // input + scanf("%s",&S); + N=strlen(S); + // count B's + c=0; + Fox(i,N) + c+=S[i]=='B'; + // output + printf("Case #%d: %c\n",t,(N/2<=c && c<=N-2)?'Y':'N'); + } + return(0); +} \ No newline at end of file diff --git a/2019/quals/leapfrog1.html b/2019/quals/leapfrog1.html new file mode 100644 index 0000000000000000000000000000000000000000..8272702f2ac8cd4078f5762e8e09af968a20c745 --- /dev/null +++ b/2019/quals/leapfrog1.html @@ -0,0 +1,84 @@ +

+This problem statement differs from that of Leapfrog Ch. 2 in only one spot, highlighted in bold below. +

+ +

+A colony of frogs peacefully resides in a pond. The colony is led by a single Alpha Frog, and also includes 0 or more Beta Frogs. +In order to be a good leader, the Alpha Frog diligently studies the high art of fractions every day. +

+ +

+There are N lilypads in a row on the pond's surface, numbered 1 to N from left to right, each of which is large enough to fit at most one frog at a time. +Today, the Alpha Frog finds itself on the leftmost lilypad, and must leap its way to the rightmost lilypad before it can begin its fractions practice. +

+ +

+The initial state of each lilypad i is described by a character Li, which is one of the following: +

+ +
    +
  • "A": Occupied by the Alpha Frog (it's guaranteed that Li = "A" if and only if i = 1)
  • +
  • "B": Occupied by a Beta Frog
  • +
  • ".": Unoccupied
  • +
+ +

+At each point in time, one of the following things may occur: +

+ +

+1) The Alpha Frog may leap over one or more lilypads immediately to its right which are occupied by Beta Frogs, and land on the next unoccupied lilypad past them, if such a lilypad exists. +The Alpha Frog must leap over at least one Beta Frog; it may not just leap to an adjacent lilypad. +Note that, unlike in Leapfrog Ch. 2, the Alpha Frog may only leap to its right. +

+ +

+2) Any Beta Frog may leap to the next lilypad to either its left or right, if such a lilypad exists and is unoccupied. +

+ +

+Assuming the frogs all cooperate, determine whether or not it's possible for the Alpha Frog to ever reach the rightmost lilypad and begin its daily fractions practice. +

+ + +

Input

+ +

+Input begins with an integer T, the number of days on which the Alpha Frog studies fractions. +For each day, there is a single line containing the length-N string L. +

+ + +

Output

+ +

+For the ith day, print a line containing "Case #i: " +followed by a single character: "Y" if the Alpha Frog can reach the rightmost lilypad, or "N" otherwise. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 500
+2 ≤ N ≤ 5,000
+

+ +

Explanation of Sample

+ +

+In the first case, the Alpha Frog can't leap anywhere. +

+ +

+In the second case, the Alpha Frog can leap over the Beta Frog to reach the rightmost lilypad. +

+ +

+In the third case, neither the Alpha Frog nor either of the Beta Frogs can leap anywhere. +

+ +

+In the fourth case, if the first Beta Frog leaps one lilypad to the left, and then the second Beta Frog also leaps one lilypad to the left, +then the Alpha Frog can leap over both of them to reach the rightmost lilypad. +

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-0,0 +1,65 @@ +**This problem statement differs from that of Leapfrog Ch. 2 in only one spot, highlighted in bold below.** + +A colony of frogs peacefully resides in a pond. The colony is led by a single +Alpha Frog, and also includes 0 or more Beta Frogs. In order to be a good +leader, the Alpha Frog diligently studies the high art of fractions every day. + +There are **N** lilypads in a row on the pond's surface, numbered 1 to **N** +from left to right, each of which is large enough to fit at most one frog at a +time. Today, the Alpha Frog finds itself on the leftmost lilypad, and must +leap its way to the rightmost lilypad before it can begin its fractions +practice. + +The initial state of each lilypad _i_ is described by a character **Li**, +which is one of the following: + + * "`A`": Occupied by the Alpha Frog (it's guaranteed that **Li** = "`A`" if and only if _i_ = 1) + * "`B`": Occupied by a Beta Frog + * "`.`": Unoccupied + +At each point in time, one of the following things may occur: + +1) The Alpha Frog may leap over one or more lilypads immediately to its right +which are occupied by Beta Frogs, and land on the next unoccupied lilypad past +them, if such a lilypad exists. The Alpha Frog must leap over at least one +Beta Frog; it may not just leap to an adjacent lilypad. **Note that, unlike in +Leapfrog Ch. 2, the Alpha Frog may only leap to its right.** + +2) Any Beta Frog may leap to the next lilypad to either its left or right, if +such a lilypad exists and is unoccupied. + +Assuming the frogs all cooperate, determine whether or not it's possible for +the Alpha Frog to ever reach the rightmost lilypad and begin its daily +fractions practice. + +### Input + +Input begins with an integer **T**, the number of days on which the Alpha Frog +studies fractions. For each day, there is a single line containing the +length-**N** string **L**. + +### Output + +For the _i_th day, print a line containing "Case #_i_: " followed by a single +character: "`Y`" if the Alpha Frog can reach the rightmost lilypad, or "`N`" +otherwise. + +### Constraints + +1 ≤ **T** ≤ 500 +2 ≤ **N** ≤ 5,000 + +### Explanation of Sample + +In the first case, the Alpha Frog can't leap anywhere. + +In the second case, the Alpha Frog can leap over the Beta Frog to reach the +rightmost lilypad. + +In the third case, neither the Alpha Frog nor either of the Beta Frogs can +leap anywhere. + +In the fourth case, if the first Beta Frog leaps one lilypad to the left, and +then the second Beta Frog also leaps one lilypad to the left, then the Alpha +Frog can leap over both of them to reach the rightmost lilypad. + diff --git a/2019/quals/leapfrog1.out b/2019/quals/leapfrog1.out new file mode 100644 index 0000000000000000000000000000000000000000..618ab92624d445867103b31a5486d27ad5f708a9 --- /dev/null +++ b/2019/quals/leapfrog1.out @@ -0,0 +1,1050 @@ +Case #1: N +Case #2: Y +Case #3: N +Case #4: Y +Case #5: N +Case #6: Y +Case #7: N +Case #8: Y +Case #9: N +Case #10: N +Case #11: Y +Case #12: Y +Case #13: Y +Case #14: Y +Case #15: N +Case #16: Y +Case #17: N +Case #18: N +Case #19: N +Case #20: N +Case #21: N +Case #22: N +Case #23: N +Case #24: Y +Case #25: N +Case #26: N +Case #27: N +Case #28: N +Case #29: N +Case #30: N +Case #31: N +Case #32: N +Case #33: N +Case #34: Y +Case #35: Y +Case #36: N +Case #37: N +Case #38: N +Case #39: N +Case #40: N +Case #41: N +Case #42: N +Case #43: N +Case #44: N +Case #45: N +Case #46: N +Case #47: N +Case #48: N +Case #49: N +Case #50: N +Case #51: N +Case #52: N +Case #53: N +Case #54: N +Case #55: N +Case #56: N +Case #57: N +Case #58: N +Case #59: N +Case #60: N +Case #61: N +Case #62: N +Case #63: N +Case #64: N +Case #65: N +Case #66: Y +Case #67: N +Case #68: N +Case #69: N +Case #70: N +Case #71: N +Case #72: N +Case #73: N +Case #74: Y +Case #75: N +Case #76: N +Case #77: N +Case #78: Y +Case #79: N +Case #80: Y +Case #81: Y +Case #82: Y +Case #83: N +Case #84: N +Case #85: N +Case #86: N +Case #87: N +Case #88: N +Case #89: N +Case #90: Y +Case #91: N +Case #92: N +Case #93: N +Case #94: Y +Case #95: N +Case #96: Y +Case #97: Y +Case #98: Y +Case #99: N +Case #100: N +Case #101: N +Case #102: Y +Case #103: N +Case #104: Y +Case #105: Y +Case #106: Y +Case #107: N +Case #108: Y +Case #109: Y +Case #110: Y +Case #111: Y +Case #112: Y +Case #113: Y +Case #114: Y +Case #115: N +Case #116: N +Case #117: N +Case #118: N +Case #119: N +Case #120: N +Case #121: N +Case #122: Y +Case #123: N +Case #124: N +Case #125: N +Case #126: Y +Case #127: N +Case #128: Y +Case #129: Y +Case #130: Y +Case #131: N +Case #132: N +Case #133: N +Case #134: Y +Case #135: N +Case #136: Y +Case #137: Y +Case #138: Y +Case #139: N +Case #140: Y +Case #141: Y +Case #142: Y +Case #143: Y +Case #144: Y +Case #145: Y +Case #146: Y +Case #147: N +Case #148: N +Case #149: N +Case #150: Y +Case #151: N +Case #152: Y +Case #153: Y +Case #154: Y +Case #155: N +Case #156: Y +Case #157: Y +Case #158: Y +Case #159: Y +Case #160: Y +Case #161: Y +Case #162: Y +Case #163: N +Case #164: Y +Case #165: Y +Case #166: Y +Case #167: Y +Case #168: Y +Case #169: Y +Case #170: Y +Case #171: Y +Case #172: Y +Case #173: Y +Case #174: Y +Case #175: Y +Case #176: Y +Case #177: Y +Case #178: Y +Case #179: N +Case #180: N +Case #181: N +Case #182: N +Case #183: N +Case #184: N +Case #185: N +Case #186: Y +Case #187: N +Case #188: N +Case #189: N +Case #190: Y +Case #191: N +Case #192: Y +Case #193: Y +Case #194: Y +Case #195: N +Case #196: N +Case #197: N +Case #198: Y +Case #199: N +Case #200: Y +Case #201: Y +Case #202: Y +Case #203: N +Case #204: Y +Case #205: Y +Case #206: Y +Case #207: Y +Case #208: Y +Case #209: Y +Case #210: Y +Case #211: N +Case #212: N +Case #213: N +Case #214: Y +Case #215: N +Case #216: Y +Case #217: Y +Case #218: Y +Case #219: N +Case #220: Y +Case #221: Y +Case #222: Y +Case #223: Y +Case #224: Y +Case #225: Y +Case #226: Y +Case #227: N +Case #228: Y +Case #229: Y +Case #230: Y +Case #231: Y +Case #232: Y +Case #233: Y +Case #234: Y +Case #235: Y +Case #236: Y +Case #237: Y +Case #238: Y +Case #239: Y +Case #240: Y +Case #241: Y +Case #242: Y +Case #243: N +Case #244: N +Case #245: N +Case #246: Y +Case #247: N +Case #248: Y +Case #249: Y +Case #250: Y +Case #251: N +Case #252: Y +Case #253: Y +Case #254: Y +Case #255: Y +Case #256: Y +Case #257: Y +Case #258: Y +Case #259: N +Case #260: Y +Case #261: Y +Case #262: Y +Case #263: Y +Case #264: Y +Case #265: Y +Case #266: Y +Case #267: Y +Case #268: Y +Case #269: Y +Case #270: Y +Case #271: Y +Case #272: Y +Case #273: Y +Case #274: Y +Case #275: N +Case #276: Y +Case #277: Y +Case #278: Y +Case #279: Y +Case #280: Y +Case #281: Y +Case #282: Y +Case #283: Y +Case #284: Y +Case #285: Y +Case #286: Y +Case #287: Y +Case #288: Y +Case #289: Y +Case #290: Y +Case #291: Y +Case #292: Y +Case #293: Y +Case #294: Y +Case #295: Y +Case #296: Y +Case #297: Y +Case #298: Y +Case #299: Y +Case #300: Y +Case #301: Y +Case #302: Y +Case #303: Y +Case #304: Y +Case #305: Y +Case #306: N +Case #307: Y +Case #308: N +Case #309: Y +Case #310: Y +Case #311: N +Case #312: Y +Case #313: N +Case #314: Y +Case #315: Y +Case #316: Y +Case #317: Y +Case #318: Y +Case #319: N +Case #320: N +Case #321: N +Case #322: Y +Case #323: N +Case #324: Y +Case #325: Y +Case #326: Y +Case #327: Y +Case #328: Y +Case #329: Y +Case #330: Y +Case #331: Y +Case #332: Y +Case #333: Y +Case #334: Y +Case #335: Y +Case #336: N +Case #337: N +Case #338: Y +Case #339: Y +Case #340: N +Case #341: Y +Case #342: Y +Case #343: N +Case #344: Y +Case #345: N +Case #346: N +Case #347: Y +Case #348: Y +Case #349: Y +Case #350: N +Case #351: Y +Case #352: N +Case #353: N +Case #354: Y +Case #355: Y +Case #356: N +Case #357: Y +Case #358: Y +Case #359: N +Case #360: N +Case #361: N +Case #362: Y +Case #363: N +Case #364: N +Case #365: Y +Case #366: N +Case #367: N +Case #368: N +Case #369: Y +Case #370: Y +Case #371: Y +Case #372: N +Case #373: N +Case #374: Y +Case #375: Y +Case #376: Y +Case #377: Y +Case #378: N +Case #379: Y +Case #380: N +Case #381: N +Case #382: Y +Case #383: Y +Case #384: Y +Case #385: N +Case #386: N +Case #387: Y +Case #388: Y +Case #389: N +Case #390: N +Case #391: Y +Case #392: N +Case #393: Y +Case #394: N +Case #395: Y +Case #396: Y +Case #397: Y +Case #398: N +Case #399: Y +Case #400: N +Case #401: N +Case #402: Y +Case #403: Y +Case #404: Y +Case #405: N +Case #406: N +Case #407: N +Case #408: Y +Case #409: Y +Case #410: Y +Case #411: N +Case #412: Y +Case #413: Y +Case #414: Y +Case #415: N +Case #416: Y +Case #417: N +Case #418: Y +Case #419: N +Case #420: N +Case #421: N +Case #422: N +Case #423: Y +Case #424: Y +Case #425: N +Case #426: N +Case #427: N +Case #428: Y +Case #429: Y +Case #430: N +Case #431: N +Case #432: Y +Case #433: Y +Case #434: Y +Case #435: N +Case #436: N +Case #437: Y +Case #438: N +Case #439: N +Case #440: N +Case #441: N +Case #442: Y +Case #443: N +Case #444: Y +Case #445: N +Case #446: N +Case #447: N +Case #448: N +Case #449: N +Case #450: Y +Case #451: N +Case #452: Y +Case #453: Y +Case #454: Y +Case #455: N +Case #456: N +Case #457: N +Case #458: Y +Case #459: N +Case #460: Y +Case #461: N +Case #462: N +Case #463: N +Case #464: N +Case #465: N +Case #466: N +Case #467: Y +Case #468: N +Case #469: Y +Case #470: N +Case #471: Y +Case #472: N +Case #473: N +Case #474: N +Case #475: N +Case #476: N +Case #477: Y +Case #478: Y +Case #479: Y +Case #480: N +Case #481: N +Case #482: N +Case #483: Y +Case #484: Y +Case #485: Y +Case #486: Y +Case #487: N +Case #488: N +Case #489: N +Case #490: N +Case #491: N +Case #492: Y +Case #493: Y +Case #494: N +Case #495: Y +Case #496: Y +Case #497: Y +Case #498: Y +Case #499: N +Case #500: Y +Case #501: Y +Case #502: N +Case #503: N +Case #504: N +Case #505: N +Case #506: N +Case #507: N +Case #508: N +Case #509: Y +Case #510: N +Case #511: N +Case #512: N +Case #513: N +Case #514: N +Case #515: N +Case #516: N +Case #517: Y +Case #518: Y +Case #519: Y +Case #520: Y +Case #521: N +Case #522: N +Case #523: N +Case #524: N +Case #525: Y +Case #526: Y +Case #527: Y +Case #528: Y +Case #529: N +Case #530: N +Case #531: Y +Case #532: Y +Case #533: N +Case #534: Y +Case #535: Y +Case #536: Y +Case #537: N +Case #538: N +Case #539: Y +Case #540: N +Case #541: Y +Case #542: N +Case #543: Y +Case #544: Y +Case #545: N +Case #546: N +Case #547: Y +Case #548: Y +Case #549: N +Case #550: Y +Case #551: N +Case #552: Y +Case #553: N +Case #554: N +Case #555: Y +Case #556: N +Case #557: N +Case #558: Y +Case #559: N +Case #560: Y +Case #561: Y +Case #562: Y +Case #563: N +Case #564: Y +Case #565: N +Case #566: Y +Case #567: Y +Case #568: N +Case #569: N +Case #570: Y +Case #571: Y +Case #572: N +Case #573: N +Case #574: Y +Case #575: Y +Case #576: Y +Case #577: Y +Case #578: N +Case #579: N +Case #580: Y +Case #581: N +Case #582: N +Case #583: Y +Case #584: Y +Case #585: Y +Case #586: Y +Case #587: Y +Case #588: Y +Case #589: N +Case #590: N +Case #591: N +Case #592: N +Case #593: Y +Case #594: N +Case #595: Y +Case #596: Y +Case #597: N +Case #598: Y +Case #599: Y +Case #600: Y +Case #601: N +Case #602: N +Case #603: Y +Case #604: Y +Case #605: N +Case #606: Y +Case #607: Y +Case #608: N +Case #609: Y +Case #610: Y +Case #611: N +Case #612: N +Case #613: N +Case #614: N +Case #615: N +Case #616: N +Case #617: N +Case #618: Y +Case #619: Y +Case #620: Y +Case #621: N +Case #622: Y +Case #623: N +Case #624: N +Case #625: N +Case #626: Y +Case #627: Y +Case #628: Y +Case #629: Y +Case #630: Y +Case #631: Y +Case #632: Y +Case #633: Y +Case #634: Y +Case #635: Y +Case #636: N +Case #637: N +Case #638: Y +Case #639: N +Case #640: Y +Case #641: Y +Case #642: N +Case #643: N +Case #644: N +Case #645: Y +Case #646: N +Case #647: Y +Case #648: Y +Case #649: Y +Case #650: N +Case #651: Y +Case #652: N +Case #653: N +Case #654: Y +Case #655: Y +Case #656: N +Case #657: N +Case #658: Y +Case #659: Y +Case #660: Y +Case #661: N +Case #662: N +Case #663: N +Case #664: N +Case #665: Y +Case #666: N +Case #667: Y +Case #668: Y +Case #669: Y +Case #670: Y +Case #671: N +Case #672: Y +Case #673: Y +Case #674: Y +Case #675: Y +Case #676: Y +Case #677: Y +Case #678: N +Case #679: Y +Case #680: Y +Case #681: N +Case #682: N +Case #683: N +Case #684: Y +Case #685: Y +Case #686: N +Case #687: N +Case #688: Y +Case #689: Y +Case #690: N +Case #691: Y +Case #692: N +Case #693: Y +Case #694: N +Case #695: N +Case #696: Y +Case #697: Y +Case #698: N +Case #699: Y +Case #700: N +Case #701: Y +Case #702: N +Case #703: N +Case #704: Y +Case #705: Y +Case #706: Y +Case #707: N +Case #708: Y +Case #709: N +Case #710: N +Case #711: N +Case #712: N +Case #713: N +Case #714: N +Case #715: Y +Case #716: N +Case #717: N +Case #718: N +Case #719: Y +Case #720: Y +Case #721: N +Case #722: Y +Case #723: N +Case #724: N +Case #725: Y +Case #726: N +Case #727: Y +Case #728: N +Case #729: Y +Case #730: Y +Case #731: N +Case #732: N +Case #733: Y +Case #734: N +Case #735: Y +Case #736: Y +Case #737: Y +Case #738: N +Case #739: Y +Case #740: N +Case #741: Y +Case #742: Y +Case #743: N +Case #744: N +Case #745: Y +Case #746: N +Case #747: N +Case #748: Y +Case #749: Y +Case #750: N +Case #751: Y +Case #752: N +Case #753: Y +Case #754: N +Case #755: Y +Case #756: Y +Case #757: N +Case #758: N +Case #759: N +Case #760: Y +Case #761: N +Case #762: N +Case #763: N +Case #764: Y +Case #765: Y +Case #766: N +Case #767: N +Case #768: Y +Case #769: N +Case #770: N +Case #771: Y +Case #772: Y +Case #773: Y +Case #774: N +Case #775: N +Case #776: N +Case #777: N +Case #778: Y +Case #779: Y +Case #780: N +Case #781: Y +Case #782: N +Case #783: N +Case #784: N +Case #785: Y +Case #786: Y +Case #787: Y +Case #788: Y +Case #789: Y +Case #790: N +Case #791: N +Case #792: N +Case #793: N +Case #794: N +Case #795: N +Case #796: N +Case #797: N +Case #798: N +Case #799: Y +Case #800: N +Case #801: N +Case #802: Y +Case #803: Y +Case #804: N +Case #805: N +Case #806: Y +Case #807: Y +Case #808: Y +Case #809: Y +Case #810: Y +Case #811: Y +Case #812: Y +Case #813: N +Case #814: Y +Case #815: N +Case #816: Y +Case #817: N +Case #818: Y +Case #819: Y +Case #820: Y +Case #821: Y +Case #822: Y +Case #823: N +Case #824: N +Case #825: Y +Case #826: N +Case #827: N +Case #828: N +Case #829: Y +Case #830: Y +Case #831: Y +Case #832: N +Case #833: Y +Case #834: N +Case #835: Y +Case #836: Y +Case #837: N +Case #838: Y +Case #839: Y +Case #840: Y +Case #841: Y +Case #842: Y +Case #843: Y +Case #844: Y +Case #845: N +Case #846: N +Case #847: N +Case #848: N +Case #849: N +Case #850: N +Case #851: N +Case #852: Y +Case #853: Y +Case #854: Y +Case #855: N +Case #856: N +Case #857: N +Case #858: N +Case #859: N +Case #860: Y +Case #861: N +Case #862: Y +Case #863: Y +Case #864: N +Case #865: N +Case #866: N +Case #867: N +Case #868: N +Case #869: N +Case #870: N +Case #871: N +Case #872: N +Case #873: Y +Case #874: Y +Case #875: N +Case #876: Y +Case #877: N +Case #878: Y +Case #879: N +Case #880: Y +Case #881: N +Case #882: N +Case #883: N +Case #884: N +Case #885: Y +Case #886: Y +Case #887: N +Case #888: Y +Case #889: N +Case #890: Y +Case #891: N +Case #892: Y +Case #893: Y +Case #894: Y +Case #895: N +Case #896: Y +Case #897: N +Case #898: N +Case #899: N +Case #900: N +Case #901: Y +Case #902: Y +Case #903: Y +Case #904: N +Case #905: N +Case #906: Y +Case #907: Y +Case #908: Y +Case #909: Y +Case #910: N +Case #911: N +Case #912: N +Case #913: Y +Case #914: N +Case #915: N +Case #916: N +Case #917: Y +Case #918: Y +Case #919: N +Case #920: Y +Case #921: N +Case #922: N +Case #923: Y +Case #924: Y +Case #925: Y +Case #926: Y +Case #927: Y +Case #928: N +Case #929: Y +Case #930: Y +Case #931: Y +Case #932: Y +Case #933: Y +Case #934: Y +Case #935: Y +Case #936: Y +Case #937: N +Case #938: Y +Case #939: N +Case #940: N +Case #941: N +Case #942: Y +Case #943: N +Case #944: Y +Case #945: Y +Case #946: Y +Case #947: N +Case #948: Y +Case #949: N +Case #950: N +Case #951: N +Case #952: N +Case #953: N +Case #954: N +Case #955: N +Case #956: N +Case #957: Y +Case #958: Y +Case #959: Y +Case #960: N +Case #961: N +Case #962: Y +Case #963: Y +Case #964: Y +Case #965: N +Case #966: Y +Case #967: N +Case #968: Y +Case #969: Y +Case #970: N +Case #971: N +Case #972: N +Case #973: N +Case #974: Y +Case #975: N +Case #976: N +Case #977: N +Case #978: Y +Case #979: N +Case #980: N +Case #981: N +Case #982: Y +Case #983: Y +Case #984: Y +Case #985: N +Case #986: Y +Case #987: N +Case #988: Y +Case #989: N +Case #990: N +Case #991: N +Case #992: N +Case #993: N +Case #994: N +Case #995: Y +Case #996: N +Case #997: Y +Case #998: N +Case #999: N +Case #1000: N +Case #1001: N +Case #1002: N +Case #1003: Y +Case #1004: Y +Case #1005: N +Case #1006: Y +Case #1007: Y +Case #1008: N +Case #1009: N +Case #1010: Y +Case #1011: N +Case #1012: Y +Case #1013: Y +Case #1014: N +Case #1015: Y +Case #1016: Y +Case #1017: Y +Case #1018: Y +Case #1019: Y +Case #1020: N +Case #1021: N +Case #1022: N +Case #1023: N +Case #1024: Y +Case #1025: Y +Case #1026: Y +Case #1027: Y +Case #1028: N +Case #1029: N +Case #1030: Y +Case #1031: N +Case #1032: N +Case #1033: N +Case #1034: Y +Case #1035: N +Case #1036: Y +Case #1037: N +Case #1038: Y +Case #1039: Y +Case #1040: N +Case #1041: N +Case #1042: N +Case #1043: Y +Case #1044: Y +Case #1045: Y +Case #1046: Y +Case #1047: N +Case #1048: Y +Case #1049: N +Case #1050: N diff --git a/2019/quals/leapfrog2.cpp b/2019/quals/leapfrog2.cpp new file mode 100644 index 0000000000000000000000000000000000000000..58028fc8eb2f1564f1d9038a82286ab62c9642b0 --- /dev/null +++ b/2019/quals/leapfrog2.cpp @@ -0,0 +1,112 @@ +// Leapfrog Ch. 2 +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int N; + int i,c; + char S[5005]; + // testcase loop + Read(T); + Fox1(t,T) + { + // input + scanf("%s",&S); + N=strlen(S); + // count B's + c=0; + Fox(i,N) + c+=S[i]=='B'; + // output + printf("Case #%d: %c\n",t,(min(2,N/2)<=c && c<=N-2)?'Y':'N'); + } + return(0); +} \ No newline at end of file diff --git a/2019/quals/leapfrog2.html b/2019/quals/leapfrog2.html new file mode 100644 index 0000000000000000000000000000000000000000..1f24ac87589732e8131faf131f82d3d970a2a49f --- /dev/null +++ b/2019/quals/leapfrog2.html @@ -0,0 +1,85 @@ +

+This problem statement differs from that of Leapfrog Ch. 1 in only one spot, highlighted in bold below. +

+ +

+A colony of frogs peacefully resides in a pond. The colony is led by a single Alpha Frog, and also includes 0 or more Beta Frogs. +In order to be a good leader, the Alpha Frog diligently studies the high art of fractions every day. +

+ +

+There are N lilypads in a row on the pond's surface, numbered 1 to N from left to right, each of which is large enough to fit at most one frog at a time. +Today, the Alpha Frog finds itself on the leftmost lilypad, and must leap its way to the rightmost lilypad before it can begin its fractions practice. +

+ +

+The initial state of each lilypad i is described by a character Li, which is one of the following: +

+ +
    +
  • "A": Occupied by the Alpha Frog (it's guaranteed that Li = "A" if and only if i = 1)
  • +
  • "B": Occupied by a Beta Frog
  • +
  • ".": Unoccupied
  • +
+ +

+At each point in time, one of the following things may occur: +

+ +

+1) The Alpha Frog may leap over one or more lilypads immediately to either its left or right which are occupied by Beta Frogs, +and land on the next unoccupied lilypad past them, if such a lilypad exists. +The Alpha Frog must leap over at least one Beta Frog; it may not just leap to an adjacent lilypad. +Note that, unlike in Leapfrog Ch. 1, the Alpha Frog may leap to either its left or right. +

+ +

+2) Any Beta Frog may leap to the next lilypad to either its left or right, if such a lilypad exists and is unoccupied. +

+ +

+Assuming the frogs all cooperate, determine whether or not it's possible for the Alpha Frog to ever reach the rightmost lilypad and begin its daily fractions practice. +

+ + +

Input

+ +

+Input begins with an integer T, the number of days on which the Alpha Frog studies fractions. +For each day, there is a single line containing the length-N string L. +

+ + +

Output

+ +

+For the ith day, print a line containing "Case #i: " +followed by a single character: "Y" if the Alpha Frog can reach the rightmost lilypad, or "N" otherwise. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 500
+2 ≤ N ≤ 5,000
+

+ +

Explanation of Sample

+ +

+In the first case, the Alpha Frog can't leap anywhere. +

+ +

+In the second case, the Alpha Frog can leap over the Beta Frog to reach the rightmost lilypad. +

+ +

+In the third case, neither the Alpha Frog nor either of the Beta Frogs can leap anywhere. +

+ +

+In the fourth case, if the first Beta Frog leaps one lilypad to the left, and then the second Beta Frog also leaps one lilypad to the left, +then the Alpha Frog can leap over both of them to reach the rightmost lilypad. +

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+A....B......B.......B................B.B....B.......B.B.................B...B..............B........................B.......................B..B................B.......B....B.....B............B........BB.B.B..B.........BBB...............B........................B............B.....B....B..........B...............B..........BB..............B.....................B...................B......B.........B.B...B....................B..B....B.BB.B.B......B.......B..B...B.B......BB......B..................................B...B......B....BB........................B....B........B..............B............B..B..BB....B.....B..B..B..........B...B..................................B..................B..B...............B.....B.B.B................BB........BB..........................B...........B.............................B....B.......B.B......B........B....................B............................B..................................................B..B.........B................................B....................B.........B....BB...B.BB....B.............B.......B.B.......B.....B........................................B.......B....B..BB...B................B.........B.................B............B.B......B............B...............B............B.B..............B.............B..B...........................B....B......B......................B........B...........B...................BB...........BB...........................B..B..BB.BBBB.B..........BB......B...B...........................B...B.B.....................................B.......B.....B.......B.B......................B..............B............BB..B.................B.....B........B....B..BB.......................B.....B.............................................B...B...B......B..B..B................B...B................B............B...................B.B............B......B........B..B....B.B.............B..................B....BB.............B..............B............................B........B....B..B...........B...B....B.......B....B........B.........B..B.......B..B..........B.B....B.BBB...B.............B....B.................BB..B....B.........B..........B.B.........................B.B..B...B.B.....B..........................BB..B.......................B.B.B..........B...................B........B........B.............B..........B..B..................B..........B.....B.............BB...........................B...BB...............................B..B...B.B.......B..BB...B..........................................B.BB.B....B.............B...BB.....B..BB........BB..B..B......B.B...B...........B.....B........BB..........B.....B..B..B....B.......B.......B...B.........B..................B......B.B..........B........................B.BBB............B....B.........B.....................B.................B.B................B.B.............B............B......B.B..B.............B..B....B.......B........B...................................B...................B.B.....B..B.............B............B....B.................BB.....................BB..........................................B............B..B.......B..........B...B...........BB....................................B.......................B....BB........B..B..................B..B.....B..................B....B....BB.B.......BB..........B..B..BB...........B...B...B.B.................B.........B.B..B.....BB.............................B.B.........B................BB.....B..B......B...B....B........B.B.........B....B..........B..B........................................................B...B................B.......B..........................B....B.B.....B.....B...............B............B..............B....B.............................B.............B.B........B..B.......BB........B....B.....BB...B.BBB..........B.......B.......BB...............B.........B.................B...................B.......B............B..B.............................B.....................B..BB.............BB.B.............B...BB......BB.....B..............B.B..........B.B.......B........B..B.BB..............B..........B...B........B.........BB.........B......B...B........B.....B....B......B.....B...........BB.........B.....B........................B.......B.......................B..........B.B.....BB................B.B...B...................B..BB..BB...................B.....B...B.....B..........BB.....B........B.....B............B..B.......................B.............B.B.........................................BB...........B.....B.......B..................B............B..B..................BB..................B............B...............................B....B..............BB................BB............B...........B.........B....B....B......B...........B.........................BB...B..B..................B........B.B........B....B......B...B..B...............B.......B.......BB............B......B..B....B.....B.......B..B...BB...B...B......B...B..B........B.............B.B.......B.......B...B.B.........B.......B.....B........B..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diff --git a/2019/quals/leapfrog2.md b/2019/quals/leapfrog2.md new file mode 100644 index 0000000000000000000000000000000000000000..bc161f5814b2869a91bade6fcbcc278ae755783d --- /dev/null +++ b/2019/quals/leapfrog2.md @@ -0,0 +1,66 @@ +**This problem statement differs from that of Leapfrog Ch. 1 in only one spot, highlighted in bold below.** + +A colony of frogs peacefully resides in a pond. The colony is led by a single +Alpha Frog, and also includes 0 or more Beta Frogs. In order to be a good +leader, the Alpha Frog diligently studies the high art of fractions every day. + +There are **N** lilypads in a row on the pond's surface, numbered 1 to **N** +from left to right, each of which is large enough to fit at most one frog at a +time. Today, the Alpha Frog finds itself on the leftmost lilypad, and must +leap its way to the rightmost lilypad before it can begin its fractions +practice. + +The initial state of each lilypad _i_ is described by a character **Li**, +which is one of the following: + + * "`A`": Occupied by the Alpha Frog (it's guaranteed that **Li** = "`A`" if and only if _i_ = 1) + * "`B`": Occupied by a Beta Frog + * "`.`": Unoccupied + +At each point in time, one of the following things may occur: + +1) The Alpha Frog may leap over one or more lilypads immediately to either its +left or right which are occupied by Beta Frogs, and land on the next +unoccupied lilypad past them, if such a lilypad exists. The Alpha Frog must +leap over at least one Beta Frog; it may not just leap to an adjacent lilypad. +**Note that, unlike in Leapfrog Ch. 1, the Alpha Frog may leap to either its +left or right.** + +2) Any Beta Frog may leap to the next lilypad to either its left or right, if +such a lilypad exists and is unoccupied. + +Assuming the frogs all cooperate, determine whether or not it's possible for +the Alpha Frog to ever reach the rightmost lilypad and begin its daily +fractions practice. + +### Input + +Input begins with an integer **T**, the number of days on which the Alpha Frog +studies fractions. For each day, there is a single line containing the +length-**N** string **L**. + +### Output + +For the _i_th day, print a line containing "Case #_i_: " followed by a single +character: "`Y`" if the Alpha Frog can reach the rightmost lilypad, or "`N`" +otherwise. + +### Constraints + +1 ≤ **T** ≤ 500 +2 ≤ **N** ≤ 5,000 + +### Explanation of Sample + +In the first case, the Alpha Frog can't leap anywhere. + +In the second case, the Alpha Frog can leap over the Beta Frog to reach the +rightmost lilypad. + +In the third case, neither the Alpha Frog nor either of the Beta Frogs can +leap anywhere. + +In the fourth case, if the first Beta Frog leaps one lilypad to the left, and +then the second Beta Frog also leaps one lilypad to the left, then the Alpha +Frog can leap over both of them to reach the rightmost lilypad. + diff --git a/2019/quals/leapfrog2.out b/2019/quals/leapfrog2.out new file mode 100644 index 0000000000000000000000000000000000000000..29dc75aaa6874874cfeddf5909f999442fd648de --- /dev/null +++ b/2019/quals/leapfrog2.out @@ -0,0 +1,1060 @@ +Case #1: N +Case #2: Y +Case #3: N +Case #4: Y +Case #5: Y +Case #6: Y +Case #7: N +Case #8: Y +Case #9: N +Case #10: N +Case #11: Y +Case #12: Y +Case #13: Y +Case #14: Y +Case #15: N +Case #16: Y +Case #17: N +Case #18: N +Case #19: N +Case #20: N +Case #21: N +Case #22: N +Case #23: N +Case #24: Y +Case #25: Y +Case #26: Y +Case #27: Y +Case #28: Y +Case #29: Y +Case #30: Y +Case #31: Y +Case #32: Y +Case #33: Y +Case #34: Y +Case #35: Y +Case #36: Y +Case #37: Y +Case #38: Y +Case #39: Y +Case #40: Y +Case #41: Y +Case #42: Y +Case #43: Y +Case #44: Y +Case #45: Y +Case #46: Y +Case #47: Y +Case #48: Y +Case #49: Y +Case #50: Y +Case #51: N +Case #52: N +Case #53: N +Case #54: Y +Case #55: N +Case #56: Y +Case #57: Y +Case #58: Y +Case #59: N +Case #60: Y +Case #61: Y +Case #62: Y +Case #63: Y +Case #64: Y +Case #65: Y +Case #66: Y +Case #67: N +Case #68: Y +Case #69: Y +Case #70: Y +Case #71: Y +Case #72: Y +Case #73: Y +Case #74: Y +Case #75: Y +Case #76: Y +Case #77: Y +Case #78: Y +Case #79: Y +Case #80: Y +Case #81: Y +Case #82: Y +Case #83: N +Case #84: Y +Case #85: Y +Case #86: Y +Case #87: Y +Case #88: Y +Case #89: Y +Case #90: Y +Case #91: Y +Case #92: Y +Case #93: Y +Case #94: Y +Case #95: Y +Case #96: Y +Case #97: Y +Case #98: Y +Case #99: Y +Case #100: Y +Case #101: Y +Case #102: Y +Case #103: Y +Case #104: Y +Case #105: Y +Case #106: Y +Case #107: Y +Case #108: Y +Case #109: Y +Case #110: Y +Case #111: Y +Case #112: Y +Case #113: Y +Case #114: Y +Case #115: N +Case #116: Y +Case #117: Y +Case #118: Y +Case #119: Y +Case #120: Y +Case #121: Y +Case #122: Y +Case #123: Y +Case #124: Y +Case #125: Y +Case #126: Y +Case #127: Y +Case #128: Y +Case #129: Y +Case #130: Y +Case #131: Y +Case #132: Y +Case #133: Y +Case #134: Y +Case #135: Y +Case #136: Y +Case #137: Y +Case #138: Y +Case #139: Y +Case #140: Y +Case #141: Y +Case #142: Y +Case #143: Y +Case #144: Y +Case #145: Y +Case #146: Y +Case #147: Y +Case #148: Y +Case #149: Y +Case #150: Y +Case #151: Y +Case #152: Y +Case #153: Y +Case #154: Y +Case #155: Y +Case #156: Y +Case #157: Y +Case #158: Y +Case #159: Y +Case #160: Y +Case #161: Y +Case #162: Y +Case #163: Y +Case #164: Y +Case #165: Y +Case #166: Y +Case #167: Y +Case #168: Y +Case #169: Y +Case #170: Y +Case #171: Y +Case #172: Y +Case #173: Y +Case #174: Y +Case #175: Y +Case #176: Y +Case #177: Y +Case #178: Y +Case #179: N +Case #180: Y +Case #181: Y +Case #182: Y +Case #183: Y +Case #184: Y +Case #185: Y +Case #186: Y +Case #187: Y +Case #188: Y +Case #189: Y +Case #190: Y +Case #191: Y +Case #192: Y +Case #193: Y +Case #194: Y +Case #195: Y +Case #196: Y +Case #197: Y +Case #198: Y +Case #199: Y +Case #200: Y +Case #201: Y +Case #202: Y +Case #203: Y +Case #204: Y +Case #205: Y +Case #206: Y +Case #207: Y +Case #208: Y +Case #209: Y +Case #210: Y +Case #211: Y +Case #212: Y +Case #213: Y +Case #214: Y +Case #215: Y +Case #216: Y +Case #217: Y +Case #218: Y +Case #219: Y +Case #220: Y +Case #221: Y +Case #222: Y +Case #223: Y +Case #224: Y +Case #225: Y +Case #226: Y +Case #227: Y +Case #228: Y +Case #229: Y +Case #230: Y +Case #231: Y +Case #232: Y +Case #233: Y +Case #234: Y +Case #235: Y +Case #236: Y +Case #237: Y +Case #238: Y +Case #239: Y +Case #240: Y +Case #241: Y +Case #242: Y +Case #243: Y +Case #244: Y +Case #245: Y +Case #246: Y +Case #247: Y +Case #248: Y +Case #249: Y +Case #250: Y +Case #251: Y +Case #252: Y +Case #253: Y +Case #254: Y +Case #255: Y +Case #256: Y +Case #257: Y +Case #258: Y +Case #259: Y +Case #260: Y +Case #261: Y +Case #262: Y +Case #263: Y +Case #264: Y +Case #265: Y +Case #266: Y +Case #267: Y +Case #268: Y +Case #269: Y +Case #270: Y +Case #271: Y +Case #272: Y +Case #273: Y +Case #274: Y +Case #275: Y +Case #276: Y +Case #277: Y +Case #278: Y +Case #279: Y +Case #280: Y +Case #281: Y +Case #282: Y +Case 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Y +Case #355: Y +Case #356: Y +Case #357: Y +Case #358: Y +Case #359: Y +Case #360: Y +Case #361: Y +Case #362: Y +Case #363: Y +Case #364: Y +Case #365: Y +Case #366: Y +Case #367: Y +Case #368: Y +Case #369: Y +Case #370: Y +Case #371: Y +Case #372: Y +Case #373: Y +Case #374: Y +Case #375: Y +Case #376: Y +Case #377: Y +Case #378: Y +Case #379: Y +Case #380: Y +Case #381: Y +Case #382: Y +Case #383: Y +Case #384: Y +Case #385: Y +Case #386: Y +Case #387: Y +Case #388: Y +Case #389: Y +Case #390: Y +Case #391: Y +Case #392: Y +Case #393: Y +Case #394: Y +Case #395: Y +Case #396: Y +Case #397: Y +Case #398: Y +Case #399: Y +Case #400: Y +Case #401: Y +Case #402: Y +Case #403: Y +Case #404: Y +Case #405: Y +Case #406: Y +Case #407: Y +Case #408: Y +Case #409: Y +Case #410: Y +Case #411: Y +Case #412: Y +Case #413: Y +Case #414: Y +Case #415: Y +Case #416: Y +Case #417: Y +Case #418: Y +Case #419: Y +Case #420: Y +Case #421: Y +Case #422: Y +Case #423: Y +Case #424: Y +Case #425: Y +Case #426: Y +Case #427: N +Case #428: Y +Case #429: Y +Case #430: Y +Case #431: Y +Case #432: Y +Case #433: Y +Case #434: Y +Case #435: Y +Case #436: Y +Case #437: Y +Case #438: Y +Case #439: Y +Case #440: Y +Case #441: Y +Case #442: Y +Case #443: Y +Case #444: Y +Case #445: Y +Case #446: Y +Case #447: Y +Case #448: Y +Case #449: Y +Case #450: Y +Case #451: Y +Case #452: Y +Case #453: Y +Case #454: Y +Case #455: Y +Case #456: Y +Case #457: Y +Case #458: Y +Case #459: Y +Case #460: Y +Case #461: Y +Case #462: Y +Case #463: Y +Case #464: Y +Case #465: Y +Case #466: Y +Case #467: Y +Case #468: Y +Case #469: Y +Case #470: Y +Case #471: Y +Case #472: Y +Case #473: Y +Case #474: Y +Case #475: Y +Case #476: Y +Case #477: Y +Case #478: Y +Case #479: Y +Case #480: Y +Case #481: Y +Case #482: Y +Case #483: Y +Case #484: Y +Case #485: Y +Case #486: N +Case #487: Y +Case #488: Y +Case #489: Y +Case #490: Y +Case #491: Y +Case #492: Y +Case #493: Y +Case #494: Y +Case #495: Y +Case #496: Y +Case #497: Y +Case #498: Y +Case #499: Y +Case #500: Y +Case #501: Y +Case #502: Y +Case #503: N +Case #504: Y +Case #505: Y +Case #506: Y +Case #507: Y +Case #508: Y +Case #509: Y +Case #510: Y +Case #511: N +Case #512: Y +Case #513: Y +Case #514: Y +Case #515: Y +Case #516: Y +Case #517: Y +Case #518: Y +Case #519: Y +Case #520: Y +Case #521: Y +Case #522: Y +Case #523: Y +Case #524: Y +Case #525: Y +Case #526: Y +Case #527: Y +Case #528: Y +Case #529: Y +Case #530: Y +Case #531: Y +Case #532: Y +Case #533: Y +Case #534: Y +Case #535: Y +Case #536: Y +Case #537: Y +Case #538: Y +Case #539: Y +Case #540: Y +Case #541: Y +Case #542: Y +Case #543: Y +Case #544: Y +Case #545: Y +Case #546: Y +Case #547: Y +Case #548: Y +Case #549: Y +Case #550: Y +Case #551: Y +Case #552: Y +Case #553: Y +Case #554: Y +Case #555: Y +Case #556: Y +Case #557: Y +Case #558: Y +Case #559: Y +Case #560: Y +Case #561: Y +Case #562: Y +Case #563: N +Case #564: Y +Case #565: Y +Case #566: Y +Case #567: Y +Case #568: Y +Case #569: Y +Case #570: Y +Case #571: Y +Case #572: Y +Case #573: Y +Case #574: Y +Case #575: Y +Case #576: Y +Case #577: Y +Case #578: Y +Case #579: Y +Case #580: Y +Case #581: Y +Case #582: Y +Case #583: Y +Case #584: Y +Case #585: Y +Case #586: Y +Case #587: Y +Case #588: Y +Case #589: N +Case #590: Y +Case #591: Y +Case #592: N +Case #593: Y +Case #594: Y +Case #595: Y +Case #596: Y +Case #597: Y +Case #598: Y +Case #599: Y +Case #600: Y +Case #601: Y +Case #602: Y +Case #603: Y +Case #604: Y +Case #605: Y +Case #606: Y +Case #607: Y +Case #608: Y +Case #609: Y +Case #610: Y +Case #611: Y +Case #612: N +Case #613: Y +Case #614: Y +Case #615: Y +Case #616: Y +Case #617: Y +Case #618: Y +Case #619: Y +Case #620: Y +Case #621: Y +Case #622: Y +Case #623: Y +Case #624: Y +Case #625: Y +Case #626: Y +Case #627: Y +Case #628: Y +Case #629: Y +Case #630: Y +Case #631: Y +Case #632: Y +Case #633: Y +Case #634: Y +Case #635: Y +Case #636: Y +Case #637: Y +Case #638: Y +Case #639: Y +Case #640: Y +Case #641: Y +Case #642: Y +Case #643: Y +Case #644: Y +Case #645: Y +Case #646: Y +Case #647: Y +Case #648: Y +Case #649: Y +Case #650: Y +Case #651: Y +Case #652: Y +Case #653: Y +Case #654: Y +Case #655: Y +Case #656: Y +Case #657: Y +Case #658: Y +Case #659: Y +Case #660: Y +Case #661: Y +Case #662: Y +Case #663: Y +Case #664: Y +Case #665: Y +Case #666: Y +Case #667: Y +Case #668: Y +Case #669: Y +Case #670: Y +Case #671: Y +Case #672: Y +Case #673: Y +Case #674: Y +Case #675: Y +Case #676: Y +Case #677: Y +Case #678: N +Case #679: Y +Case #680: Y +Case #681: Y +Case #682: Y +Case #683: Y +Case #684: Y +Case #685: Y +Case #686: Y +Case #687: Y +Case #688: Y +Case #689: Y +Case #690: Y +Case #691: Y +Case #692: Y +Case #693: Y +Case #694: Y +Case #695: Y +Case #696: Y +Case #697: Y +Case #698: Y +Case #699: Y +Case #700: Y +Case #701: Y +Case #702: Y +Case #703: Y +Case #704: Y +Case #705: Y +Case #706: Y +Case #707: Y +Case #708: Y +Case #709: Y +Case #710: Y +Case #711: Y +Case #712: Y +Case #713: Y +Case #714: Y +Case #715: Y +Case #716: Y +Case #717: Y +Case #718: Y +Case #719: Y +Case #720: Y +Case #721: Y +Case #722: Y +Case #723: Y +Case #724: Y +Case #725: Y +Case #726: Y +Case #727: Y +Case #728: Y +Case #729: Y +Case #730: Y +Case #731: Y +Case #732: Y +Case #733: Y +Case #734: Y +Case #735: N +Case #736: Y +Case #737: Y +Case #738: Y +Case #739: Y +Case #740: Y +Case #741: Y +Case #742: Y +Case #743: Y +Case #744: Y +Case #745: Y +Case #746: Y +Case #747: Y +Case #748: Y +Case #749: Y +Case #750: Y +Case #751: Y +Case #752: Y +Case #753: Y +Case #754: Y +Case #755: Y +Case #756: Y +Case #757: Y +Case #758: Y +Case #759: Y +Case #760: Y +Case #761: Y +Case #762: Y +Case #763: Y +Case #764: N +Case #765: Y +Case #766: Y +Case #767: Y +Case #768: Y +Case #769: Y +Case #770: Y +Case #771: Y +Case #772: Y +Case #773: Y +Case #774: Y +Case #775: Y +Case #776: Y +Case #777: N +Case #778: Y +Case #779: Y +Case #780: Y +Case #781: Y +Case #782: Y +Case #783: Y +Case #784: Y +Case #785: Y +Case #786: Y +Case #787: Y +Case #788: Y +Case #789: Y +Case #790: Y +Case #791: Y +Case #792: Y +Case #793: Y +Case #794: Y +Case #795: Y +Case #796: Y +Case #797: Y +Case #798: Y +Case #799: Y +Case #800: Y +Case #801: Y +Case #802: Y +Case #803: Y +Case #804: Y +Case #805: Y +Case #806: Y +Case #807: Y +Case #808: Y +Case #809: Y +Case #810: Y +Case #811: Y +Case #812: Y +Case #813: Y +Case #814: Y +Case #815: Y +Case #816: Y +Case #817: Y +Case #818: Y +Case #819: Y +Case #820: Y +Case #821: Y +Case #822: Y +Case #823: Y +Case #824: Y +Case #825: Y +Case #826: Y +Case #827: Y +Case #828: Y +Case #829: Y +Case #830: Y +Case #831: Y +Case #832: Y +Case #833: Y +Case #834: Y +Case #835: Y +Case #836: Y +Case #837: Y +Case #838: Y +Case #839: Y +Case #840: Y +Case #841: Y +Case #842: Y +Case #843: Y +Case #844: Y +Case #845: Y +Case #846: Y +Case #847: Y +Case #848: Y +Case #849: Y +Case #850: Y +Case #851: Y +Case #852: N +Case #853: Y +Case #854: Y +Case #855: Y +Case #856: Y +Case #857: Y +Case #858: Y +Case #859: Y +Case #860: Y +Case #861: Y +Case #862: Y +Case #863: Y +Case #864: Y +Case #865: Y +Case #866: Y +Case #867: Y +Case #868: Y +Case #869: Y +Case #870: Y +Case #871: Y +Case #872: Y +Case #873: Y +Case #874: Y +Case #875: Y +Case #876: Y +Case #877: N +Case #878: Y +Case #879: Y +Case #880: Y +Case #881: Y +Case #882: Y +Case #883: Y +Case #884: Y +Case #885: Y +Case #886: Y +Case #887: Y +Case #888: Y +Case #889: Y +Case #890: N +Case #891: Y +Case #892: Y +Case #893: Y +Case #894: Y +Case #895: Y +Case #896: Y +Case #897: Y +Case #898: Y +Case #899: Y +Case #900: Y +Case #901: Y +Case #902: Y +Case #903: Y +Case #904: Y +Case #905: Y +Case #906: Y +Case #907: Y +Case #908: Y +Case #909: Y +Case #910: Y +Case #911: Y +Case #912: Y +Case #913: Y +Case #914: Y +Case #915: Y +Case #916: Y +Case #917: Y +Case #918: Y +Case #919: Y +Case #920: Y +Case #921: N +Case #922: Y +Case #923: Y +Case #924: Y +Case #925: N +Case #926: Y +Case #927: Y +Case #928: Y +Case #929: Y +Case #930: Y +Case #931: Y +Case #932: Y +Case #933: Y +Case #934: Y +Case #935: Y +Case #936: Y +Case #937: Y +Case #938: Y +Case #939: Y +Case #940: Y +Case #941: Y +Case #942: Y +Case #943: Y +Case #944: Y +Case #945: Y +Case #946: Y +Case #947: Y +Case #948: Y +Case #949: Y +Case #950: Y +Case #951: Y +Case #952: Y +Case #953: N +Case #954: Y +Case #955: Y +Case #956: Y +Case #957: Y +Case #958: Y +Case #959: Y +Case #960: Y +Case #961: Y +Case #962: Y +Case #963: Y +Case #964: Y +Case #965: Y +Case #966: Y +Case #967: Y +Case #968: Y +Case #969: Y +Case #970: Y +Case #971: Y +Case #972: Y +Case #973: Y +Case #974: Y +Case #975: Y +Case #976: Y +Case #977: N +Case #978: Y +Case #979: Y +Case #980: Y +Case #981: Y +Case #982: Y +Case #983: Y +Case #984: N +Case #985: Y +Case #986: Y +Case #987: Y +Case #988: Y +Case #989: Y +Case #990: Y +Case #991: Y +Case #992: Y +Case #993: Y +Case #994: Y +Case #995: Y +Case #996: Y +Case #997: Y +Case #998: Y +Case #999: Y +Case #1000: Y +Case #1001: Y +Case #1002: Y +Case #1003: Y +Case #1004: Y +Case #1005: Y +Case #1006: Y +Case #1007: Y +Case #1008: Y +Case #1009: Y +Case #1010: Y +Case #1011: Y +Case #1012: Y +Case #1013: Y +Case #1014: Y +Case #1015: Y +Case #1016: Y +Case #1017: Y +Case #1018: Y +Case #1019: Y +Case #1020: Y +Case #1021: Y +Case #1022: Y +Case #1023: Y +Case #1024: Y +Case #1025: Y +Case #1026: Y +Case #1027: Y +Case #1028: Y +Case #1029: Y +Case #1030: Y +Case #1031: Y +Case #1032: Y +Case #1033: Y +Case #1034: Y +Case #1035: Y +Case #1036: Y +Case #1037: Y +Case #1038: Y +Case #1039: Y +Case #1040: Y +Case #1041: Y +Case #1042: Y +Case #1043: Y +Case #1044: Y +Case #1045: Y +Case #1046: Y +Case #1047: Y +Case #1048: Y +Case #1049: Y +Case #1050: Y +Case #1051: Y +Case #1052: Y +Case #1053: N +Case #1054: Y +Case #1055: N +Case #1056: Y +Case #1057: Y +Case #1058: Y +Case #1059: Y +Case #1060: Y diff --git a/2019/quals/mr_x.cpp b/2019/quals/mr_x.cpp new file mode 100644 index 0000000000000000000000000000000000000000..6ffeae40b062c8466d8f76a4d42519b92b9518d1 --- /dev/null +++ b/2019/quals/mr_x.cpp @@ -0,0 +1,136 @@ +// Mr. X +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +int Eval(int v1,char o,int v2) +{ + if (o=='|') + return(v1|v2); + if (o=='&') + return(v1&v2); + return(v1^v2); +} + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int i,x,ss; + char S[303],st[303]; + char res[2]; + // testcase loop + Read(T); + Fox1(t,T) + { + // input + scanf("%s",&S); + // evaluate expression for x=0 and x=1 + Fox(x,2) + { + ss=0; + Fox(i,strlen(S)) + if (S[i]==')') + { + ss-=3; + st[ss-1]=Eval(st[ss]-'0',st[ss+1],st[ss+2]-'0')+'0'; + } + else + if (S[i]=='x') + st[ss++]=x+'0'; + else + if (S[i]=='X') + st[ss++]=(1-x)+'0'; + else + st[ss++]=S[i]; + res[x]=st[0]; + } + // output + printf("Case #%d: %d\n",t,(res[0]==res[1])?0:1); + } + return(0); +} \ No newline at end of file diff --git a/2019/quals/mr_x.html b/2019/quals/mr_x.html new file mode 100644 index 0000000000000000000000000000000000000000..745732df03e89d9c4b2728ad3043152bc779e8ed --- /dev/null +++ b/2019/quals/mr_x.html @@ -0,0 +1,105 @@ +

+"There's nothing more important than x!", laughs Mr. X as he explains a Boolean expression involving a variable x to you and your classmates. +He can't go 5 minutes teaching Boolean algebra without making at least one such "joke"... +

+ +

+In Mr. X's class, you've been learning about single-variable Boolean expressions, which are made up of the variable x (and its negation), Boolean constants (True/False), and binary Boolean operators. A valid expression is a string in one of the following two forms: +

+ +

+1) A single term, which is one of the following four characters: +

    +
  • "x": The variable x
  • +
  • "X": The negation of the variable x
  • +
  • "0": The constant False
  • +
  • "1": The constant True
  • +
+

+ +

+2) A binary operator joining two valid expressions in the format "([expression][operator][expression])", with the operator being one of the following three characters: +

    +
  • "|": The OR operator (evaluating to True when at least one of its operands is True)
  • +
  • "&": The AND operator (evaluating to True when both of its operands are True)
  • +
  • "^": The XOR operator (evaluating to True when exactly one of its operands is True)
  • +
+

+ +

+For example, the following expressions are valid: +

    +
  • "1"
  • +
  • "(x^0)"
  • +
  • "((X&0)|x)"
  • +
+

+ +

+While the following expressions are invalid: +

    +
  • "(1)"
  • +
  • "x^0"
  • +
  • "(X&0|x)"
  • +
+

+ +

+An upcoming test will feature a valid expression E in the above format, which must be evaluated for a certain value of x. +However, you've been getting tired of Mr. X and his lame jokes about the importance of x, +so you're planning on hacking into his test files and changing the expression so as to make x irrelevant! +In particular, you'd like to modify as few characters as possible in E such that it ends up still being a valid expression, +but such that its overall value doesn't depend on the value of the variable x. You may only change characters in-place into different characters — you may not insert or delete characters. +

+ +

+For example, the expression "(X|(0&x))" evaluates to True if x is False, and False if x is True. +If it were to be changed into "((X&0)&1)" (by modifying its 2nd, 3rd, 4th, 6th, 7th, and 8th characters), then it would evaluate to False regardless of x's value. +Though, it's also possible to make its value independent of x by modifying fewer than 6 of its characters. +

+ +

+Given an expression E, what's the minimum number of characters which must be modified? It's possible that no characters may need to be modified at all. +

+ + +

Input

+ +

+Input begins with an integer T, the number of tests. +For each test, there is a line containing the expression E. +

+ + +

Output

+ +

+For the ith test, print a line containing "Case #i: " +followed by a single integer, the minimum number of characters to modify in E such that the result is a valid expression whose value doesn't depend on the value of x. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 500
+1 ≤ |E| ≤ 300
+

+ +

Explanation of Sample

+ +

+The first expression can, for example, be changed to "1" (and would then always evaluate to True). +

+ +

+The second expression can be left unchanged (as it always evaluates to False). +

+ +

+The third expression can be left unchanged (as it always evaluates to True). +

+ +

+The fourth expression can, for example, be changed to "((0^(X&X))|x)" (and would then always evaluate to True). +

diff --git a/2019/quals/mr_x.in b/2019/quals/mr_x.in new file mode 100644 index 0000000000000000000000000000000000000000..049ad0e86c0188d38f6f981943d213c9ba8cb501 --- /dev/null +++ b/2019/quals/mr_x.in @@ -0,0 +1,1058 @@ +1057 +X +0 +(x|1) +((1^(X&X))|x) +1 +x +((((X^(((1&0)&(1&(0&0)))^1))^(1|1))|X)&(((((0|1)|0)|(1|x))|(((0|(1|X))&x)&x))^(((0|x)&x)&(x|(X|0))))) +((x|x)&(x|x)) +((x&x)|(x&x)) +(0|0) +(0|1) +(0|x) +(0|X) +(1|0) +(1|1) +(1|x) +(1|X) +(x|0) +(x|1) +(x|x) +(x|X) +(X|0) +(X|1) +(X|x) +(X|X) +(0&0) +(0&1) +(0&x) +(0&X) +(1&0) +(1&1) +(1&x) +(1&X) +(x&0) +(x&1) +(x&x) +(x&X) +(X&0) +(X&1) +(X&x) +(X&X) +(0^0) +(0^1) +(0^x) +(0^X) +(1^0) +(1^1) +(1^x) +(1^X) +(x^0) +(x^1) +(x^x) +(x^X) +(X^0) +(X^1) +(X^x) +(X^X) 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+((((1^X)&(X|0))&(1&(((1&1)^1)^(((1&0)^X)^1))))^(((x|X)|((X&(X&(x|(0&x))))^(x&(x^(1&(1|(x|(x|X))))))))|(((((X|((x|x)^(0|1)))&(0|x))&x)&(1|X))&(x&(x^x))))) +(X|(((x^(1&0))^x)&(X|(x&1)))) +((x&(X^X))^((((((x&(1^X))&1)&(1&(X|X)))|(((0&(x|0))&((X|X)^(x^1)))&((X^x)^0)))^((((X^0)&(X^(1|X)))^(((0|x)&(X&X))&((X|x)^((0^(0^0))|((x|(1&X))^1)))))&((1|X)&(x&x))))|(X^x))) +((((1|0)|(0&(((X&X)|(x&X))^(X^0))))&(1&(X^(x&0))))&(((((X|X)|x)|((x|(0^x))&(X^x)))|1)^((((((X|1)|1)|(1^X))&((1&((0&(X|X))^((((1&1)|(x^x))&(x&X))^1)))^(X|(0&(X&X)))))|(X|(X|x)))^(((0^x)|x)|(((x^0)&(1^x))|1))))) +(((((1^(((x^X)^(0|X))&(x&x)))|x)&x)|((X&X)&0))^((((((0&1)|0)|((x&(x|0))^(X^(X&1))))|(((X&X)&(1&0))&(1^0)))^(((1|(X|0))&(((X&(1^0))^x)&(0^X)))&X))^(0^(X&(x&X))))) +((((((X&(x&((1&X)&x)))|((((1&(X&x))^1)^(x|1))&0))&(x^(((((1&X)&0)&1)&(1^x))|X)))^(1^((((x&X)|X)&(0|x))|(1^1))))|((1^(((1&(1|x))^0)^(((X|(0^(0&X)))|x)&(X&(0&0)))))^((X^(1^(0|x)))^((0|X)|(0^x)))))&(((0^0)^((0^X)&(0&(0|(1^x)))))^(X&((1|X)|(x&0))))) +((x&0)|((1^1)|1)) +((1^((0&0)&x))|(((X&X)&X)&((1^x)^(((1&(1^x))|X)^(x|(0&1)))))) +(((x^(x|((X&0)^1)))&(x&(X^0)))&((((X^X)&x)|(1&0))|0)) +((((X&(1^1))&(1|(1|x)))|(((X|X)&(x^(x&x)))|X))|(((((x^(0^1))&((x|((0|0)&0))|0))^(X&(0^(0|1))))^(0|((1^x)^x)))|((1&0)^((X^(((X|X)|((x|1)^(0^0)))^x))|((((((1&0)|1)&X)|1)|((x|(x&X))|X))&((X|((x|x)&((1|X)|0)))^0)))))) +(((1&x)|(((X^x)&(((0&x)^x)^1))|((((x|1)|X)&(X^((x|((1^0)&1))&(X&1))))^(x&1))))|(((((((x|0)^(1^1))&X)|x)|(0|(0&x)))|((((X&x)|(X|0))^(1|X))^(1^(((1&X)|(0|X))|(0^X)))))^(((x|(X|(1&x)))|(X|(X&1)))&(X^((1^1)|x))))) +(((((1|1)|(((0|((x|X)^x))&0)^(x|(((X|0)|x)&(X|0)))))&((1&(X|x))^x))^(X^(X|x)))^((0|(((((x|(x|x))&1)|(x&X))|X)|((0&(0&0))&(X|(1&(0&x))))))^((((x&(x&X))|(1&1))&((X|(1&(X|x)))^1))^(((((1|x)|1)^1)^(0&(x&0)))^((1^X)^(x&X)))))) +((((0^(0^x))&(((0^0)^(x^((X&1)|x)))&(1^((1&1)|(X|((X|0)^0))))))&(1&0))|((0^(X^(0^0)))&(X^x))) +((((0^x)^(((0^X)&(x&(0^1)))&(X&X)))&((1|1)|X))|((0|((1^0)&0))&(X^X))) +(((((x&0)|0)|X)^(((1&(0&x))|(1&x))^((X|(x&1))^X)))&(((((X|X)^(((x^x)^0)&X))|(0|(0|((1&(X^x))&0))))&((0&x)|((x&1)^(X|0))))&(1|(1&(1|1))))) +((((((0^X)|(X^1))^(((X^x)^(x|X))&(0&((x&X)^(X^1)))))|((x^X)&0))&(((((1|x)|(1|(1&1)))^((0|X)|X))|((0^0)|(1&1)))&(((0^x)^x)^(1^X))))&((0&((x^(X|x))&X))^((x|(1^1))|1))) +((((x&(((X|1)&X)&(0^(1&(x&(x|1))))))&((((x^1)|((0^x)|(X|x)))&(0&x))^(0^x)))&(X^x))^(((((1&X)|x)|(0&(X^1)))^((1|((0^(X|0))&(X^(1&(X|(1&x))))))&x))&(x|(X&1)))) +(((((X^((0^0)|0))^(1&((x&1)^x)))^0)&(((X^((1|X)|X))|((1&x)^(((x&0)&((x^X)|x))|(x&1))))|(X&(((X^(1|X))&(1&x))^(((X^0)&(1^(0&0)))^(X&x))))))^(((((X^(x|(X^0)))|(((x&0)&1)&X))^(X|(0|(1&X))))|(X|(0|0)))^0)) +(((1&x)^((((1|X)^(1&1))|1)^1))^((((1|X)|(x&x))&(1|0))|(((((x|X)^X)&1)^((0&X)^1))^(1^((0|X)&1))))) +(((0&x)|0)|((0|(1^X))|(1&x))) +((((((((x&0)|0)^(0^0))^((((x^1)^((X|(x&x))^0))^((x^(x^0))^(x&X)))&((0|((X&1)^1))&((0|(1|x))^1))))&x)&((X|x)|((1|((0&0)&X))|((x^(0&0))&(X^((x|1)|1))))))^((1&((0&(X^1))|1))^(((X^X)|(X&0))|((X|(x^(x&0)))^((0&0)&(X^(1|(X|X))))))))|(0|(1|X))) +((((((X|((1|X)^(X^X)))^(((((x&(x|X))^(0|(x^X)))|x)^0)&(((1^X)&(0|((1^0)|0)))^((x^(x|1))^0))))|(x|x))|((((X&(1^x))|(X|X))|((0&X)&(1|(1^X))))&((1|(0|1))^X)))^1)|(((X&(0&X))^((X|x)^(1^(x|0))))|(((1^((x|1)|x))^((0|x)^0))&(1^(0&x))))) +(((((((0&1)&X)&((1&(X^(x^1)))|X))|((0^0)|(x^x)))&X)|((((((1|0)|1)&0)|((x&x)&x))&((((0|0)&x)^((X&x)^(((0&x)|(X^x))|(x^(1&1)))))&((0|x)^((1&0)^(1|x)))))^((x^(0|X))^X)))|((1&0)&X)) diff --git a/2019/quals/mr_x.md b/2019/quals/mr_x.md new file mode 100644 index 0000000000000000000000000000000000000000..25faa091e8e5aaa6716aa1aa845a74a1b787f5a3 --- /dev/null +++ b/2019/quals/mr_x.md @@ -0,0 +1,84 @@ +"There's nothing more important than x!", laughs Mr. X as he explains a +Boolean expression involving a variable x to you and your classmates. He can't +go 5 minutes teaching Boolean algebra without making at least one such +"joke"... + +In Mr. X's class, you've been learning about single-variable Boolean +expressions, which are made up of the variable x (and its negation), Boolean +constants (True/False), and binary Boolean operators. A valid expression is a +string in one of the following two forms: + +1) A single term, which is one of the following four characters: + + * "`x`": The variable x + * "`X`": The negation of the variable x + * "`0`": The constant False + * "`1`": The constant True + +2) A binary operator joining two valid expressions in the format +"`([expression][operator][expression])`", with the operator being one of the +following three characters: + + * "|": The OR operator (evaluating to True when at least one of its operands is True) + * "&": The AND operator (evaluating to True when both of its operands are True) + * "^": The XOR operator (evaluating to True when exactly one of its operands is True) + +For example, the following expressions are **valid**: + + * "`1`" + * "`(x^0)`" + * "`((X&0)|x)`" + +While the following expressions are **invalid**: + + * "`(1)`" + * "`x^0`" + * "`(X&0|x)`" + +An upcoming test will feature a valid expression **E** in the above format, +which must be evaluated for a certain value of x. However, you've been getting +tired of Mr. X and his lame jokes about the importance of x, so you're +planning on hacking into his test files and changing the expression so as to +make x irrelevant! In particular, you'd like to modify as few characters as +possible in **E** such that it ends up still being a valid expression, but +such that its overall value doesn't depend on the value of the variable x. You +may only change characters in-place into different characters — you may not +insert or delete characters. + +For example, the expression "`(X|(0&x))`" evaluates to True if x is False, and +False if x is True. If it were to be changed into "`((X&0)&1)`" (by modifying +its 2nd, 3rd, 4th, 6th, 7th, and 8th characters), then it would evaluate to +False regardless of x's value. Though, it's also possible to make its value +independent of x by modifying fewer than 6 of its characters. + +Given an expression **E**, what's the minimum number of characters which must +be modified? It's possible that no characters may need to be modified at all. + +### Input + +Input begins with an integer **T**, the number of tests. For each test, there +is a line containing the expression **E**. + +### Output + +For the _i_th test, print a line containing "Case #_i_: " followed by a single +integer, the minimum number of characters to modify in **E** such that the +result is a valid expression whose value doesn't depend on the value of x. + +### Constraints + +1 ≤ **T** ≤ 500 +1 ≤ |**E**| ≤ 300 + +### Explanation of Sample + +The first expression can, for example, be changed to "`1`" (and would then +always evaluate to True). + +The second expression can be left unchanged (as it always evaluates to False). + +The third expression can be left unchanged (as it always evaluates to True). + +The fourth expression can, for example, be changed to "`((0^(X&X))|x)`" (and +would then always evaluate to True). + diff --git a/2019/quals/mr_x.out b/2019/quals/mr_x.out new file mode 100644 index 0000000000000000000000000000000000000000..f9474796ae7dc8d433fa3aae59b4941d2f704def --- /dev/null +++ b/2019/quals/mr_x.out @@ -0,0 +1,1057 @@ +Case #1: 1 +Case #2: 0 +Case #3: 0 +Case #4: 1 +Case #5: 0 +Case #6: 1 +Case #7: 1 +Case #8: 1 +Case #9: 1 +Case #10: 0 +Case #11: 0 +Case #12: 1 +Case #13: 1 +Case #14: 0 +Case #15: 0 +Case #16: 0 +Case #17: 0 +Case #18: 1 +Case #19: 0 +Case #20: 1 +Case #21: 0 +Case #22: 1 +Case #23: 0 +Case #24: 0 +Case #25: 1 +Case #26: 0 +Case #27: 0 +Case #28: 0 +Case #29: 0 +Case #30: 0 +Case #31: 0 +Case #32: 1 +Case #33: 1 +Case #34: 0 +Case #35: 1 +Case #36: 1 +Case #37: 0 +Case #38: 0 +Case #39: 1 +Case #40: 0 +Case #41: 1 +Case #42: 0 +Case #43: 0 +Case #44: 1 +Case #45: 1 +Case #46: 0 +Case #47: 0 +Case #48: 1 +Case #49: 1 +Case #50: 1 +Case #51: 1 +Case #52: 0 +Case #53: 0 +Case #54: 1 +Case #55: 1 +Case #56: 0 +Case #57: 0 +Case #58: 0 +Case #59: 0 +Case #60: 0 +Case #61: 1 +Case #62: 0 +Case #63: 0 +Case #64: 1 +Case #65: 1 +Case #66: 0 +Case #67: 1 +Case #68: 1 +Case #69: 0 +Case #70: 1 +Case #71: 0 +Case #72: 0 +Case #73: 1 +Case #74: 1 +Case #75: 0 +Case #76: 0 +Case #77: 0 +Case #78: 0 +Case #79: 0 +Case #80: 0 +Case #81: 1 +Case #82: 0 +Case #83: 1 +Case #84: 0 +Case #85: 0 +Case #86: 0 +Case #87: 0 +Case #88: 0 +Case #89: 0 +Case #90: 0 +Case #91: 0 +Case #92: 1 +Case #93: 0 +Case #94: 0 +Case #95: 1 +Case #96: 1 +Case #97: 1 +Case #98: 0 +Case #99: 1 +Case #100: 0 +Case #101: 1 +Case #102: 1 +Case #103: 0 +Case #104: 0 +Case #105: 0 +Case #106: 0 +Case #107: 0 +Case #108: 1 +Case #109: 0 +Case #110: 0 +Case #111: 1 +Case #112: 0 +Case #113: 0 +Case #114: 1 +Case #115: 0 +Case #116: 0 +Case #117: 1 +Case #118: 0 +Case #119: 0 +Case #120: 0 +Case #121: 0 +Case #122: 0 +Case #123: 0 +Case #124: 1 +Case #125: 1 +Case #126: 0 +Case #127: 0 +Case #128: 1 +Case #129: 0 +Case #130: 0 +Case #131: 1 +Case #132: 0 +Case #133: 1 +Case #134: 1 +Case #135: 1 +Case #136: 0 +Case #137: 1 +Case #138: 0 +Case #139: 1 +Case #140: 1 +Case #141: 0 +Case #142: 1 +Case #143: 1 +Case #144: 1 +Case #145: 1 +Case #146: 1 +Case #147: 1 +Case #148: 1 +Case #149: 0 +Case #150: 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b/2019/quals/service_trees.cpp @@ -0,0 +1,196 @@ +// Trees as a Service +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +#define MAXN 60 +#define MAXM 120 + +int N,M; +int X[MAXM],Y[MAXM],Z[MAXM],P[MAXN]; + +bool BuildTree(int par,vector nodes) +{ + int s=Sz(nodes); + int i,j,k,a,b,c; + bool here[MAXN]={0}; + bool good; + Fox(i,s) + here[nodes[i]]=1; + // consider each possible root + Fox(i,s) + { + // compute nodes which must or must not be in the same subtree + int r=nodes[i]; + vector con[MAXN]; + set badp; + vector > subtrees; + bool used[MAXN]={0}; + Fox(j,M) + if (here[a=X[j]] && here[b=Y[j]] && here[c=Z[j]]) + if (a==r || b==r) + { + // LCA of pair including root must be equal to root + if (c!=r) + goto Bad; + } + else + if (c==r) + { + // pair with LCA equal to root must be in different subtrees + badp.insert(mp(a,b)); + badp.insert(mp(b,a)); + } + else + { + // otherwise, triple must be in the same subtree + con[a].pb(b); + con[b].pb(a); + con[a].pb(c); + con[c].pb(a); + } + // floodfill to compute subtrees + Fox(j,s) + if (j!=i && !used[k=nodes[j]]) + { + vector subtree; + queue Q; + Q.push(k),used[k]=1; + while (!Q.empty()) + { + k=Q.front(),Q.pop(); + subtree.pb(k); + Fox(a,Sz(con[k])) + if (!used[b=con[k][a]]) + Q.push(b),used[b]=1; + } + Fox(a,Sz(subtree)) + Fox(b,a) + if (badp.count(mp(subtree[a],subtree[b]))) + goto Bad; + subtrees.pb(subtree); + } + // recursively attempt to build each subtree + P[r]=par; + Fox(j,Sz(subtrees)) + if (!BuildTree(r,subtrees[j])) + return(0); + return(1); +Bad:; + } + return(0); +} + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int i; + // testcase loop + Read(T); + Fox1(t,T) + { + // input + Read(N),Read(M); + Fox(i,M) + Read(X[i]),Read(Y[i]),Read(Z[i]),X[i]--,Y[i]--,Z[i]--; + // recursively build tree, and output + Fill(P,-1); + vector nodes; + Fox(i,N) + nodes.pb(i); + printf("Case #%d: ",t); + if (!BuildTree(-1,nodes)) + printf("Impossible\n"); + else + { + Fox(i,N) + printf("%d%c",P[i]+1,(i==N-1)?'\n':' '); + } + } + return(0); +} \ No newline at end of file diff --git a/2019/quals/service_trees.html b/2019/quals/service_trees.html new file mode 100644 index 0000000000000000000000000000000000000000..f0cc3cfecf8e660e6356dc22894e5bd1dacd272d --- /dev/null +++ b/2019/quals/service_trees.html @@ -0,0 +1,70 @@ +

+Carlos is hoping to strike it rich with his new consulting firm, Carlos +Structures Industries (CSI). With a solid mission statement and a can-do +attitude, he's sure to succeed in the wide world of bespoke data structures. +

+ +

+"Our vision is to synergistically leverage our core competencies to deliver +competitive market solutions that assertively meet our clients' needs." +

+ +

+His first client, the well-known translation firm Treehouse, is looking to +update their logo. Treehouse wants their logo to be a rooted tree with +N nodes numbered 1 through N. They have a rough idea of what the tree should +look like, but they want Carlos to finish fleshing it out. In particular, +they have M requirements, the ith of which states that the +lowest common ancestor +of nodes Xi and Yi must be node Zi. +

+ +

+Carlos's goal is to find any valid tree consistent with all of these requirements +if possible, or to determine that no such tree exists. +

+ + +

Input

+ +

+Input begins with an integer T, the number of tree designs. +For each design, there is first a line containing the space-separated integers N and M. +Then M lines follow, the ith of which contains the space-separated integers +Xi, Yi, and Zi. + +

+ + +

Output

+ +

+For the ith design, print a line containing "Case #i: " +followed by a description of a valid rooted tree if possible, or the string "Impossible" if no valid tree exists. +A tree description is N space-separated integers, the jth of which is node j's parent (or 0 if node j is the root). +

+ + +

Constraints

+ +

+1 ≤ T ≤ 100
+2 ≤ N ≤ 60
+1 ≤ M ≤ 120
+1 ≤ Xi, Yi, ZiN
+XiYi +

+ +

Explanation of Sample

+ +

+In the first case, the LCA of nodes 1 and 2 in the chosen tree is 3, as required. This is the only valid output for this case. +

+ +

+In the third case, "2 3 0 3" would also be accepted, while no other outputs would be. +

+ +

+In the fifth and sixth cases, multiple possible outputs would be accepted. +

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b/2019/quals/service_trees.md @@ -0,0 +1,50 @@ +Carlos is hoping to strike it rich with his new consulting firm, Carlos +Structures Industries (CSI). With a solid mission statement and a can-do +attitude, he's sure to succeed in the wide world of bespoke data structures. + +_ "Our vision is to synergistically leverage our core competencies to deliver +competitive market solutions that assertively meet our clients' needs." _ + +His first client, the well-known translation firm Treehouse, is looking to +update their logo. Treehouse wants their logo to be a rooted tree with **N** +nodes numbered 1 through **N**. They have a rough idea of what the tree should +look like, but they want Carlos to finish fleshing it out. In particular, they +have **M** requirements, the _i_th of which states that the [lowest common +ancestor](https://en.wikipedia.org/wiki/Lowest_common_ancestor) of nodes +**Xi** and **Yi** must be node **Zi**. + +Carlos's goal is to find any valid tree consistent with all of these +requirements if possible, or to determine that no such tree exists. + +### Input + +Input begins with an integer **T**, the number of tree designs. For each +design, there is first a line containing the space-separated integers **N** +and **M**. Then **M** lines follow, the _i_th of which contains the space- +separated integers **Xi**, **Yi**, and **Zi**. + +### Output + +For the _i_th design, print a line containing "Case #_i_: " followed by a +description of a valid rooted tree if possible, or the string "Impossible" if +no valid tree exists. A tree description is **N** space-separated integers, +the _j_th of which is node _j_'s parent (or 0 if node _j_ is the root). + +### Constraints + +1 ≤ **T** ≤ 100 +2 ≤ **N** ≤ 60 +1 ≤ **M** ≤ 120 +1 ≤ **Xi**, **Yi**, **Zi** ≤ **N** +**Xi** ≠ **Yi** + +### Explanation of Sample + +In the first case, the LCA of nodes 1 and 2 in the chosen tree is 3, as +required. This is the only valid output for this case. + +In the third case, "2 3 0 3" would also be accepted, while no other outputs +would be. + +In the fifth and sixth cases, multiple possible outputs would be accepted. + diff --git a/2019/quals/service_trees.out b/2019/quals/service_trees.out new file mode 100644 index 0000000000000000000000000000000000000000..b5ce759c0051cde8f1e4974567ee728e7b7ae45d --- /dev/null +++ b/2019/quals/service_trees.out @@ -0,0 +1,507 @@ +Case #1: 3 3 0 +Case #2: Impossible +Case #3: 3 0 2 3 +Case #4: Impossible +Case #5: 2 0 6 5 2 5 5 +Case #6: 7 10 12 12 10 0 6 6 12 7 8 6 +Case #7: Impossible +Case #8: 14 45 7 7 14 7 14 53 0 1 50 53 14 9 14 53 53 1 4 1 14 7 14 1 4 14 53 1 14 4 45 4 9 4 7 14 14 4 14 7 1 53 7 14 53 14 4 7 14 7 14 7 1 7 1 1 14 4 14 4 +Case #9: 17 45 14 45 22 14 30 45 53 45 39 45 14 0 17 14 14 17 14 14 57 39 41 47 14 39 17 14 27 39 14 14 45 14 45 47 14 30 14 45 45 14 39 45 14 14 45 57 17 53 17 14 14 14 48 38 22 45 14 14 +Case #10: 53 9 9 11 32 55 11 9 32 0 9 11 55 48 48 53 32 11 48 11 53 9 32 48 9 32 48 32 40 32 32 10 9 53 11 48 48 55 11 53 55 10 53 9 53 48 53 32 32 48 48 48 48 32 35 11 55 32 9 9 +Case #11: Impossible +Case #12: 4 9 25 25 17 32 2 4 45 4 25 4 25 25 25 17 25 25 45 8 25 25 9 4 0 25 9 25 9 4 4 4 25 9 4 4 9 55 25 55 25 4 9 4 4 36 25 4 9 4 4 9 13 4 17 4 7 9 25 35 +Case #13: Impossible +Case #14: Impossible +Case #15: Impossible +Case #16: 6 23 6 13 13 57 22 13 22 13 22 22 0 59 59 22 13 6 57 13 42 13 13 57 22 36 13 6 22 22 6 23 23 57 22 13 9 22 22 16 6 57 28 16 13 6 6 9 36 23 22 57 13 6 22 22 22 13 23 22 +Case #17: 15 6 15 47 28 15 28 47 47 15 47 37 47 47 47 37 15 15 47 39 47 37 47 46 37 47 55 53 47 39 15 15 47 55 15 6 6 15 15 39 11 6 58 15 39 47 0 47 15 15 15 6 55 35 37 60 55 17 47 37 +Case #18: Impossible +Case #19: Impossible +Case #20: 39 29 41 9 9 0 13 13 39 40 34 41 41 40 41 13 13 40 41 41 13 41 13 41 13 40 13 39 39 13 6 41 39 41 30 41 34 41 40 41 6 +Case #21: Impossible +Case #22: 4 6 0 6 2 3 +Case #23: 35 3 35 35 12 35 26 3 10 12 35 35 35 2 2 10 2 30 13 10 2 31 30 3 0 2 35 30 10 2 2 2 30 2 25 2 35 2 35 +Case #24: 19 20 9 5 9 9 5 19 0 5 5 9 19 9 20 5 5 19 3 5 5 9 9 5 20 9 9 5 5 2 9 +Case #25: Impossible +Case #26: 3 6 55 44 6 0 6 55 6 6 6 6 55 6 6 6 55 22 6 54 22 54 6 6 12 55 6 6 54 44 6 6 44 6 44 6 54 55 49 6 54 6 6 6 6 54 6 10 55 6 55 22 12 6 6 39 +Case #27: Impossible +Case #28: Impossible +Case #29: Impossible +Case #30: Impossible +Case #31: Impossible +Case #32: Impossible +Case #33: 0 1 42 14 43 5 1 1 1 42 1 5 1 42 42 14 1 42 39 42 42 9 1 14 42 1 1 1 42 1 1 42 42 1 14 1 1 1 1 1 42 1 42 +Case #34: 0 12 23 23 12 23 23 23 20 17 23 1 1 1 23 1 12 12 1 12 1 1 1 1 +Case #35: 0 5 2 6 1 1 2 1 +Case #36: 26 3 1 26 3 24 1 29 1 1 26 1 1 5 26 26 26 3 26 1 3 26 5 26 3 0 26 26 1 28 26 1 26 1 26 +Case #37: Impossible +Case #38: 0 1 25 1 1 25 1 25 1 1 1 9 25 25 25 1 25 25 1 25 1 1 1 27 1 9 25 27 1 25 1 1 25 25 27 25 1 25 1 25 1 1 25 +Case #39: 16 26 26 26 26 7 26 17 16 26 7 26 16 26 0 26 16 26 26 7 7 17 7 26 26 15 26 +Case #40: Impossible +Case #41: 41 41 36 29 29 10 0 41 41 26 41 22 33 26 10 36 41 26 22 41 36 33 22 41 22 41 41 41 22 41 22 7 26 41 41 41 41 22 26 26 7 +Case #42: Impossible +Case #43: Impossible +Case #44: 3 3 4 0 6 3 +Case #45: Impossible +Case #46: Impossible +Case #47: 23 53 0 53 53 9 53 53 53 9 53 9 23 16 53 9 23 53 9 9 53 53 9 23 53 53 9 9 3 23 53 9 53 53 9 16 9 53 53 53 9 9 53 53 53 53 9 53 53 53 3 9 3 3 53 +Case #48: 34 0 34 34 34 34 34 34 14 34 34 34 15 34 34 34 34 34 34 34 28 10 34 34 34 8 28 34 15 28 8 14 34 2 34 34 34 2 30 +Case #49: 17 13 7 20 17 13 1 17 1 7 9 1 9 9 17 1 0 13 20 1 13 13 17 17 +Case #50: 17 3 4 0 3 30 3 4 3 17 4 24 24 3 3 3 16 4 3 16 16 10 22 3 17 4 17 4 3 17 +Case #51: Impossible +Case #52: 0 25 1 25 22 30 25 3 18 18 1 25 3 22 25 22 25 2 2 1 3 3 25 18 3 18 30 3 18 25 3 +Case #53: 10 34 34 0 4 4 43 43 43 43 43 4 34 10 4 43 34 4 4 43 43 4 4 34 43 7 43 34 4 43 4 4 20 43 3 10 31 34 31 20 4 4 4 4 4 4 3 4 43 4 4 43 +Case #54: Impossible +Case #55: 8 8 40 8 10 28 2 10 28 40 10 0 10 10 4 10 12 35 40 10 35 35 40 4 4 40 12 10 35 2 4 10 40 28 8 3 40 40 10 12 20 +Case #56: 5 12 12 0 16 3 16 10 10 12 1 16 11 12 10 4 10 13 +Case #57: Impossible +Case #58: Impossible +Case #59: 41 33 6 1 17 23 6 41 39 3 39 41 41 41 41 41 0 41 39 30 17 23 41 41 23 39 23 30 41 41 39 41 41 39 17 41 17 41 43 43 17 23 23 +Case #60: 36 0 36 36 2 2 56 2 2 41 2 2 2 36 2 41 2 2 2 2 36 2 36 2 41 2 36 2 36 2 4 2 19 2 19 2 2 2 2 2 36 2 55 41 56 2 9 10 10 36 2 2 2 2 4 55 2 +Case #61: 0 1 31 1 1 2 1 2 18 1 2 1 1 1 1 49 1 2 1 2 2 49 49 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 16 16 1 1 2 1 49 1 2 2 1 18 +Case #62: Impossible +Case #63: 37 0 26 2 2 24 27 24 24 26 24 26 26 27 37 26 24 24 2 41 2 26 2 2 42 24 24 27 24 26 41 24 24 24 26 27 24 24 24 24 24 27 24 24 26 +Case #64: Impossible +Case #65: Impossible +Case #66: 22 0 23 2 2 23 2 2 23 27 23 23 23 26 27 2 26 27 27 2 2 23 2 2 2 27 22 23 2 2 27 27 23 2 2 23 23 27 27 23 23 23 23 2 23 27 2 27 2 2 23 23 +Case #67: 0 33 1 33 33 14 33 44 33 33 33 33 4 44 33 14 13 13 33 33 9 9 44 4 33 44 33 33 4 4 33 4 1 44 9 43 14 44 1 27 44 33 4 9 27 44 +Case #68: 5 5 5 5 0 5 14 5 31 5 5 5 5 5 5 14 14 23 36 5 23 23 14 15 5 5 14 5 23 23 14 23 5 38 5 23 5 23 5 14 5 5 5 +Case #69: 22 7 13 12 10 22 0 12 22 7 26 22 26 26 22 26 26 22 22 22 22 26 22 13 22 7 22 7 26 +Case #70: 0 1 6 3 4 1 +Case #71: 35 35 20 45 0 5 20 17 17 35 5 27 16 17 27 45 45 45 5 35 17 35 16 17 17 16 17 45 5 5 45 45 5 16 16 17 5 5 5 5 45 45 5 17 5 5 16 5 +Case #72: 29 0 9 22 46 36 29 15 15 2 46 2 36 2 36 15 34 2 36 15 36 15 6 15 22 44 36 15 2 15 24 15 2 24 15 29 36 2 2 2 6 2 29 15 2 15 15 15 36 34 2 34 36 2 2 34 +Case #73: 25 33 36 0 33 15 33 33 26 4 33 15 4 4 33 4 4 33 4 15 5 15 33 28 28 4 15 33 25 4 4 33 4 33 33 26 28 26 4 25 4 4 +Case #74: 5 3 6 13 11 5 3 13 1 3 0 11 2 +Case #75: 40 3 36 2 17 14 36 36 24 40 17 39 16 36 24 24 10 24 28 28 24 24 24 40 40 18 16 36 36 36 36 36 24 14 24 24 24 36 24 0 24 +Case #76: 26 43 13 43 34 34 9 34 43 43 26 9 26 34 34 26 34 9 43 9 26 9 26 43 26 43 26 43 9 28 26 9 26 9 43 21 0 9 21 26 26 34 37 43 34 34 43 26 21 43 34 21 34 43 26 43 +Case #77: Impossible +Case #78: Impossible +Case #79: 2 7 2 1 7 11 0 10 2 15 2 16 11 7 7 11 16 15 +Case #80: 2 0 2 6 7 7 2 +Case #81: Impossible +Case #82: Impossible +Case #83: Impossible +Case #84: 0 5 5 1 1 5 4 +Case #85: Impossible +Case #86: Impossible +Case #87: Impossible +Case #88: Impossible +Case #89: Impossible +Case #90: Impossible +Case #91: 4 12 2 12 4 0 9 6 6 4 13 9 3 6 5 13 +Case #92: 9 28 28 28 9 0 6 6 28 30 9 30 28 30 30 37 9 30 37 28 6 32 6 9 6 30 32 30 37 6 24 28 30 6 9 30 30 30 24 30 30 6 +Case #93: Impossible +Case #94: Impossible +Case #95: Impossible +Case #96: Impossible +Case #97: Impossible +Case #98: Impossible +Case #99: Impossible +Case #100: 19 21 15 32 21 19 5 19 19 19 32 34 33 32 32 32 28 21 33 32 41 19 32 33 32 33 32 32 32 32 32 19 0 32 32 32 15 6 32 21 28 19 32 +Case #101: Impossible +Case #102: Impossible +Case #103: 5 1 5 2 0 +Case #104: 26 26 32 26 34 11 11 49 11 11 36 11 37 11 32 18 32 11 5 11 11 36 34 26 0 11 32 11 36 32 13 11 28 11 28 25 32 49 17 49 34 36 11 11 34 21 21 11 13 32 +Case #105: 18 5 26 18 0 26 5 31 25 4 26 26 22 31 26 18 26 5 9 3 29 5 26 18 3 5 26 26 31 3 4 5 +Case #106: 3 11 11 7 21 11 11 11 23 21 22 11 0 22 22 19 11 7 21 22 3 13 11 7 21 21 11 13 21 7 21 13 +Case #107: 4 17 4 0 4 8 8 4 4 18 5 4 6 4 8 3 8 3 4 17 +Case #108: 21 20 1 19 19 20 21 10 19 20 2 10 19 21 19 20 19 6 0 19 19 19 1 21 19 19 19 21 21 +Case #109: Impossible +Case #110: 7 0 14 2 2 2 2 14 2 31 2 2 2 2 2 2 31 2 31 2 2 2 2 17 14 2 2 2 2 2 2 14 2 2 14 31 2 14 2 2 14 2 14 14 43 14 2 17 31 2 14 53 2 2 2 +Case #111: Impossible +Case #112: Impossible +Case #113: 11 32 5 11 11 17 11 0 8 11 8 8 8 5 8 8 11 11 8 8 11 11 5 11 11 11 8 11 8 8 8 8 11 +Case #114: 48 48 48 0 4 4 9 48 48 4 4 43 4 48 22 48 43 48 43 48 4 48 4 48 4 4 22 22 39 48 48 14 22 48 22 48 48 48 4 4 48 4 4 48 43 4 48 4 22 4 48 22 39 4 22 4 22 22 +Case #115: 11 3 10 24 3 10 8 3 3 24 8 22 10 3 8 3 10 10 8 17 24 10 17 0 17 10 8 11 8 17 8 +Case #116: 5 0 2 2 2 +Case #117: Impossible +Case #118: 15 9 4 0 13 4 11 4 13 11 8 5 3 4 9 +Case #119: Impossible +Case #120: 44 32 0 3 3 44 32 3 32 32 40 32 32 32 32 44 3 44 3 24 3 3 44 44 3 3 44 3 3 44 48 3 32 44 32 3 44 32 44 44 44 44 44 32 32 44 3 32 32 44 32 +Case #121: 14 16 11 9 14 5 9 14 1 16 14 14 14 0 14 1 9 +Case #122: 15 10 2 0 2 2 10 10 11 4 3 15 2 6 2 10 15 15 +Case #123: Impossible +Case #124: 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 0 20 43 43 20 43 43 43 43 49 43 20 43 43 43 43 43 6 43 43 20 49 43 20 35 43 43 1 20 43 43 50 43 6 43 20 43 +Case #125: 12 12 12 0 18 12 4 12 6 12 18 4 4 12 6 12 6 12 12 12 12 +Case #126: 28 0 2 28 2 28 2 2 2 2 28 39 23 2 28 28 2 2 2 28 2 28 28 28 2 28 2 2 28 6 2 28 28 4 28 2 2 2 28 2 28 28 4 28 2 +Case #127: Impossible +Case #128: Impossible +Case #129: 7 22 16 22 0 12 12 22 22 5 7 22 22 22 12 15 16 12 22 12 12 5 5 22 5 15 5 22 7 12 5 22 12 12 12 16 12 12 5 12 4 5 22 12 5 5 5 4 7 22 +Case #130: 7 7 6 7 7 29 0 29 25 2 25 27 7 29 29 27 29 27 8 7 29 28 7 13 27 28 7 13 7 29 +Case #131: 0 13 13 1 22 21 22 14 22 13 22 13 21 20 21 22 20 20 14 1 20 20 20 +Case #132: Impossible +Case #133: 0 1 45 1 1 1 1 11 1 1 45 1 1 1 1 1 1 1 1 45 25 45 1 45 45 1 1 11 1 11 1 1 11 1 45 45 1 11 1 1 1 1 25 11 1 45 45 1 1 11 1 45 1 +Case #134: 7 12 13 0 7 7 4 13 7 13 13 13 7 7 13 +Case #135: 0 1 1 1 52 1 1 1 4 1 1 52 1 1 1 1 1 1 1 4 52 4 52 1 4 1 4 1 1 4 1 1 1 1 8 1 52 1 4 4 1 15 1 1 1 1 52 1 1 8 1 4 1 1 4 +Case #136: 22 25 12 3 25 15 20 20 24 22 22 0 27 18 22 3 8 20 4 3 22 3 22 22 20 22 3 +Case #137: 21 12 21 12 19 19 12 12 12 12 12 5 23 15 5 12 21 5 21 15 0 19 12 +Case #138: 55 55 44 21 55 51 55 13 36 55 55 55 55 55 55 58 55 36 55 44 51 51 51 13 51 55 55 55 55 44 0 51 31 55 31 51 36 51 13 21 36 13 51 12 37 55 55 58 51 21 13 55 55 31 31 37 12 44 55 +Case #139: Impossible +Case #140: Impossible +Case #141: Impossible +Case #142: Impossible +Case #143: 12 17 18 13 19 17 14 16 12 14 17 13 0 12 7 14 13 12 16 3 +Case #144: Impossible +Case #145: 20 0 20 20 2 20 46 20 46 16 46 20 46 20 20 20 20 2 2 2 46 20 20 20 20 20 2 20 46 46 20 46 20 20 20 20 46 2 46 46 46 20 20 20 20 20 20 +Case #146: Impossible +Case #147: 5 11 19 16 4 16 19 16 0 4 14 5 4 8 16 9 14 8 16 9 +Case #148: 49 32 11 8 0 11 55 55 8 20 5 5 32 11 8 49 11 11 8 11 8 11 8 11 8 8 8 11 5 20 22 8 8 5 11 8 11 8 11 11 32 8 11 5 11 11 5 17 8 8 11 8 11 49 22 5 11 +Case #149: 13 13 31 0 13 13 13 31 13 13 28 13 4 13 13 31 28 13 13 13 50 13 28 13 13 13 13 13 13 13 28 31 13 31 13 4 13 13 13 13 31 13 31 13 13 28 28 4 50 13 13 28 28 13 39 31 13 13 13 +Case #150: Impossible +Case #151: 5 6 0 5 3 3 +Case #152: Impossible +Case #153: 2 11 0 3 11 10 6 11 1 14 3 11 10 3 1 +Case #154: 13 11 13 5 10 9 11 11 5 11 0 9 5 13 14 +Case #155: 23 18 18 18 18 18 28 28 28 23 22 3 16 18 23 7 13 28 22 1 28 18 28 28 18 23 18 0 +Case #156: 4 17 36 7 17 4 16 17 7 4 16 0 4 4 16 17 12 4 31 16 4 4 4 16 17 4 4 17 17 14 16 16 4 7 4 17 4 12 14 17 4 17 +Case #157: 9 9 22 0 9 22 9 37 22 22 9 22 22 9 2 11 2 22 9 4 11 4 4 9 9 22 4 9 11 43 22 9 9 4 58 3 22 22 4 22 9 58 9 22 4 9 9 13 11 11 9 37 15 22 9 9 58 22 +Case #158: Impossible +Case #159: 37 10 27 37 37 37 37 27 10 27 27 37 0 37 37 27 37 10 27 37 37 25 27 37 27 27 13 37 10 10 27 27 10 37 10 37 27 27 27 37 37 27 27 27 10 37 +Case #160: Impossible +Case #161: Impossible +Case #162: Impossible +Case #163: 17 17 6 0 17 4 4 4 4 4 17 6 4 17 6 4 6 4 4 6 6 6 4 6 19 +Case #164: 14 14 14 14 29 14 14 33 23 14 18 29 29 0 7 14 14 14 28 18 14 29 29 14 33 39 14 14 7 14 14 14 14 14 14 14 14 28 18 +Case #165: Impossible +Case #166: 5 5 5 10 10 7 1 7 6 0 +Case #167: 8 11 10 11 6 0 3 12 6 6 10 5 +Case #168: 15 0 15 15 2 10 2 15 15 15 15 21 2 15 2 2 2 2 15 2 15 15 15 15 15 10 15 15 15 2 2 2 15 +Case #169: 13 28 34 12 34 11 34 11 11 0 13 34 10 28 10 34 11 34 11 13 10 11 13 12 10 11 36 34 11 11 34 34 34 11 28 11 10 10 11 13 12 +Case #170: 2 0 2 2 2 2 2 2 2 2 2 2 2 2 47 2 2 2 2 2 2 2 2 2 12 2 2 2 47 2 2 47 2 47 2 2 2 2 2 44 2 2 2 2 2 2 44 +Case #171: 29 15 29 15 15 15 2 15 34 37 29 37 29 29 29 29 29 29 15 37 15 29 15 5 29 15 29 29 37 29 29 29 15 13 29 8 0 29 15 +Case #172: 5 1 4 0 4 4 18 4 4 4 4 4 18 4 4 19 18 4 4 4 4 4 4 18 4 +Case #173: Impossible +Case #174: Impossible +Case #175: 10 19 1 10 19 4 10 10 1 0 1 22 10 10 10 10 1 10 1 49 10 49 10 47 47 1 1 17 47 19 49 49 1 19 19 19 47 1 1 1 19 19 1 11 10 10 49 10 4 11 +Case #176: Impossible +Case #177: Impossible +Case #178: 6 3 6 6 2 7 0 +Case #179: 16 3 0 31 31 3 31 31 29 5 5 29 31 31 31 5 31 31 31 5 31 31 5 14 20 20 31 31 3 5 3 3 3 31 28 29 23 +Case #180: 4 3 0 2 3 +Case #181: 0 41 1 1 41 1 41 1 1 27 41 43 41 1 29 1 1 1 41 32 41 41 42 27 41 1 41 42 41 41 1 1 1 42 1 41 1 27 1 41 32 41 1 41 1 27 41 1 +Case #182: 43 9 9 7 21 21 25 0 21 43 21 6 21 21 9 39 9 22 7 46 22 8 21 43 21 21 43 21 21 21 46 21 43 9 9 46 21 6 21 39 16 21 46 21 39 25 21 21 +Case #183: 3 9 9 0 9 5 9 9 4 3 5 5 9 3 9 9 9 +Case #184: 14 28 11 28 28 28 18 6 6 28 15 29 15 6 28 25 15 6 20 11 24 29 6 6 11 28 11 0 14 28 6 +Case #185: 21 21 1 1 21 21 0 4 21 21 20 21 20 4 1 1 1 1 1 1 7 1 +Case #186: 34 12 5 34 0 12 34 15 27 34 5 5 5 34 5 12 5 34 5 5 29 5 34 27 12 12 34 27 34 12 27 5 34 12 5 18 5 +Case #187: 13 13 36 19 0 30 40 40 13 5 5 5 5 44 30 13 23 5 5 23 40 43 13 5 36 12 5 5 36 5 5 5 23 5 5 5 44 30 5 23 19 36 5 5 40 36 36 37 5 36 +Case #188: Impossible +Case #189: Impossible +Case #190: 15 23 30 0 23 12 26 30 23 39 30 16 16 16 23 26 30 26 26 26 16 1 16 23 16 4 18 26 16 26 23 23 16 26 39 30 26 26 12 16 16 16 30 26 16 30 16 3 4 1 26 15 +Case #191: Impossible +Case #192: Impossible +Case #193: 4 23 5 14 13 4 14 6 14 3 3 6 14 0 4 3 12 1 4 1 1 5 13 +Case #194: 22 1 22 24 3 23 19 4 4 26 22 2 23 1 4 30 30 22 22 5 19 0 22 22 30 22 4 26 24 4 +Case #195: Impossible +Case #196: 6 6 27 38 13 13 13 27 5 5 13 6 27 13 31 6 13 13 13 13 13 27 6 0 13 13 24 27 13 13 6 27 6 27 13 38 27 13 27 +Case #197: 0 1 37 1 37 37 1 1 1 1 1 1 55 1 1 1 1 1 1 6 1 37 1 37 37 37 37 1 37 55 37 1 1 1 1 1 1 1 1 57 37 1 1 1 1 1 37 1 6 1 37 1 1 1 1 1 37 +Case #198: 12 1 5 7 0 5 12 5 5 13 1 5 1 12 5 1 +Case #199: 10 0 22 10 25 25 10 2 10 25 14 10 10 23 10 8 8 22 25 22 8 25 10 23 8 22 +Case #200: Impossible +Case #201: Impossible +Case #202: 2 11 11 1 2 15 11 10 11 1 0 2 11 1 2 +Case #203: 13 8 13 13 13 11 13 13 8 11 13 15 0 4 13 13 13 15 13 +Case #204: 2 10 2 2 6 9 12 9 10 0 10 9 +Case #205: 0 1 28 39 48 37 37 9 28 37 37 37 36 1 37 37 48 37 37 39 37 37 36 28 21 28 37 39 48 1 28 28 37 37 37 28 1 36 48 48 37 37 1 48 37 28 48 37 +Case #206: 42 31 31 31 0 31 42 31 22 20 31 42 21 30 5 20 31 31 20 31 31 20 31 20 21 5 5 5 31 31 5 20 31 5 31 5 20 5 30 5 31 31 31 31 21 +Case #207: Impossible +Case #208: 0 19 6 19 21 1 1 19 19 19 6 1 19 1 1 19 6 6 6 6 20 19 1 6 6 6 19 1 19 19 1 1 +Case #209: 9 11 0 2 13 9 11 11 13 9 9 9 3 9 2 2 13 13 20 9 13 3 13 2 9 9 9 13 +Case #210: 4 4 7 0 4 7 4 4 4 +Case #211: 6 3 5 1 6 16 16 12 16 12 12 16 12 1 6 0 16 6 3 +Case #212: 10 15 15 25 25 55 55 15 1 0 25 4 4 15 1 25 10 25 25 15 15 37 55 25 15 25 15 25 37 37 25 25 25 25 25 15 15 25 4 9 25 15 1 32 37 25 55 37 1 25 15 1 1 15 4 25 9 +Case #213: Impossible +Case #214: 14 0 5 6 6 7 15 7 12 15 10 6 4 15 2 12 10 5 +Case #215: Impossible +Case #216: 16 15 5 5 16 16 15 7 15 8 7 16 15 7 16 0 7 5 15 15 +Case #217: 0 1 1 1 1 1 50 1 1 1 47 1 1 53 50 1 1 50 50 1 1 1 50 1 4 53 50 1 47 4 50 50 49 1 1 50 50 1 1 1 1 1 1 1 1 1 50 50 50 1 49 1 1 +Case #218: 13 7 16 18 29 5 26 13 0 18 23 24 7 24 7 13 13 7 7 16 13 9 7 23 16 9 5 23 16 +Case #219: 2 0 6 2 2 13 2 13 2 2 2 13 2 +Case #220: Impossible +Case #221: 4 4 4 0 4 4 5 +Case #222: 19 12 7 12 12 7 0 7 7 14 7 19 8 7 7 7 5 12 14 +Case #223: 2 4 4 9 16 16 16 16 6 2 2 16 6 7 16 0 16 12 +Case #224: 20 3 0 20 17 3 20 10 13 15 15 3 17 15 20 15 15 17 3 2 3 26 20 17 30 3 30 15 25 26 3 +Case #225: 19 16 8 19 15 0 15 19 22 19 19 15 22 3 6 19 15 19 15 16 1 3 +Case #226: 40 40 58 47 47 40 2 47 16 47 47 47 40 47 40 0 40 40 16 58 40 40 16 40 58 40 58 47 47 47 40 40 40 40 40 16 16 40 40 16 40 15 40 16 40 2 40 40 2 40 40 40 40 40 15 58 40 40 40 +Case #227: 3 1 0 2 4 +Case #228: Impossible +Case #229: 3 3 6 6 4 0 3 1 +Case #230: 11 27 22 11 27 20 27 33 33 39 27 39 27 27 31 11 26 39 21 11 27 39 27 26 26 33 0 27 16 23 11 27 27 39 33 11 33 39 33 33 11 39 31 23 +Case #231: Impossible +Case #232: 4 14 4 24 24 24 4 0 13 24 7 4 27 13 24 4 4 4 4 4 7 13 13 8 4 4 24 27 24 +Case #233: Impossible +Case #234: 5 17 4 15 9 9 5 15 0 15 5 15 15 11 17 14 9 9 5 14 +Case #235: 17 47 47 0 4 4 47 7 4 21 4 42 47 4 4 4 47 47 4 4 17 4 4 4 4 47 21 4 4 47 4 4 47 39 21 4 4 4 47 47 4 47 4 4 4 4 4 42 47 +Case #236: Impossible +Case #237: 15 15 17 31 7 30 23 29 7 11 17 11 9 20 17 15 30 31 17 29 7 31 0 11 30 17 17 2 15 23 7 +Case #238: 7 32 6 7 25 7 0 7 7 12 7 32 7 2 25 25 7 26 12 7 15 8 32 22 7 25 7 7 8 8 5 25 +Case #239: 6 7 6 6 9 0 1 9 6 1 6 +Case #240: Impossible +Case #241: Impossible +Case #242: 20 20 36 28 28 28 20 0 20 20 28 16 20 16 20 33 28 20 24 8 31 24 20 20 24 33 31 20 31 8 28 24 20 36 20 16 +Case #243: 14 5 11 15 8 14 14 13 13 5 5 8 14 0 5 2 +Case #244: Impossible +Case #245: 18 0 45 7 2 2 45 37 2 45 18 2 45 7 18 2 45 45 2 2 37 37 18 45 2 2 2 18 2 45 45 2 45 45 45 45 18 2 2 18 2 18 2 45 2 2 2 45 37 2 2 2 +Case #246: Impossible +Case #247: 6 13 14 1 1 0 13 14 11 2 10 13 1 6 +Case #248: 0 20 9 20 9 1 20 2 20 5 20 20 1 20 20 20 20 1 1 1 1 5 20 20 20 12 1 +Case #249: 16 15 7 16 26 16 0 16 7 7 15 10 10 16 16 7 15 16 7 10 10 16 7 7 7 16 7 10 24 16 11 +Case #250: 24 24 18 23 7 9 18 18 12 9 18 7 12 18 18 20 23 0 14 23 7 18 24 18 7 +Case #251: Impossible +Case #252: Impossible +Case #253: 40 0 52 49 30 52 52 40 2 30 2 28 18 49 2 2 49 33 2 52 28 2 52 52 2 2 52 52 40 52 52 52 52 28 30 49 52 33 52 30 30 34 52 18 2 2 34 2 30 2 2 2 52 2 2 +Case #254: 2 10 11 0 4 2 11 11 10 11 4 10 4 10 +Case #255: 4 10 8 0 3 8 11 4 6 1 1 +Case #256: Impossible +Case #257: 23 23 23 23 23 0 6 23 6 6 14 23 23 23 14 6 6 14 6 6 6 28 6 6 28 23 6 23 23 14 6 6 6 6 23 23 6 23 6 25 6 6 +Case #258: 3 1 0 3 4 +Case #259: Impossible +Case #260: Impossible +Case #261: 17 17 17 36 17 2 17 36 17 2 32 43 36 36 0 17 36 17 23 17 17 17 38 36 17 31 43 36 17 36 21 21 36 36 32 15 36 17 17 36 17 36 3 36 31 +Case #262: 7 7 14 7 7 14 14 7 7 14 7 7 14 0 7 7 15 8 2 +Case #263: 3 6 6 3 6 0 +Case #264: Impossible +Case #265: 9 9 14 9 31 9 9 9 19 19 19 14 19 19 19 19 19 0 18 9 9 19 19 19 18 19 9 19 31 19 19 9 18 19 9 +Case #266: Impossible +Case #267: 12 6 11 5 6 13 13 6 6 12 10 6 0 13 18 6 5 7 6 5 15 6 +Case #268: 20 20 2 20 26 19 18 14 20 20 8 19 6 6 19 19 19 6 20 0 19 2 6 19 19 19 18 19 26 20 2 19 18 19 20 19 8 20 +Case #269: 11 12 15 14 12 11 11 11 5 5 0 11 14 12 9 14 +Case #270: Impossible +Case #271: Impossible +Case #272: 10 37 31 10 10 10 5 31 10 28 10 31 28 28 31 31 28 28 0 5 31 28 5 31 28 31 5 19 31 10 5 10 10 5 28 37 28 31 28 31 31 10 28 5 28 31 28 28 31 5 5 28 5 +Case #273: 14 14 0 1 14 14 8 14 14 3 14 8 1 3 +Case #274: Impossible +Case #275: 33 20 19 0 19 36 27 27 27 34 4 15 4 34 27 11 4 14 15 27 11 4 15 34 34 14 11 36 4 20 4 27 15 20 27 34 33 11 27 +Case #276: Impossible +Case #277: 0 1 1 1 29 1 29 21 21 29 5 8 1 2 1 8 1 2 29 1 39 1 1 2 1 29 1 22 1 1 1 21 1 1 1 2 1 21 10 21 1 +Case #278: 3 8 0 11 3 8 4 1 1 4 1 +Case #279: Impossible +Case #280: 7 33 35 10 10 33 8 36 10 33 6 2 28 9 10 18 9 33 18 10 33 10 36 33 33 33 33 10 9 33 33 33 0 33 9 33 33 +Case #281: Impossible +Case #282: 18 5 4 5 0 1 5 5 5 13 5 17 4 5 4 13 5 17 11 28 17 5 4 5 1 4 5 1 +Case #283: Impossible +Case #284: Impossible +Case #285: 15 15 15 15 59 12 0 12 15 15 15 15 33 12 7 15 15 16 12 15 7 15 18 34 12 15 15 46 16 16 44 15 59 16 15 15 15 15 15 12 44 7 12 34 16 12 15 15 15 15 15 46 15 15 15 44 15 15 15 +Case #286: Impossible +Case #287: 40 15 40 15 15 15 15 13 37 13 4 15 0 13 13 4 4 13 4 40 4 13 15 13 9 4 1 13 25 15 4 15 15 37 13 15 15 13 13 37 4 4 13 13 37 +Case #288: 25 25 0 25 3 25 25 25 3 25 25 25 25 25 44 3 25 25 3 25 25 3 25 3 3 25 25 25 3 33 25 25 25 3 25 25 3 25 25 25 3 4 25 25 4 25 25 25 33 25 25 25 25 44 25 44 3 25 +Case #289: 3 0 2 3 4 2 3 2 4 2 2 24 3 20 27 3 24 2 2 24 2 24 2 16 4 3 2 2 20 2 3 2 3 3 +Case #290: 44 47 44 47 44 23 35 47 44 23 44 16 16 1 47 1 2 16 23 16 23 6 44 44 44 16 15 35 23 44 16 44 0 44 44 16 47 16 44 16 35 47 44 33 47 44 16 16 2 47 6 +Case #291: 32 32 0 3 36 33 3 33 33 33 3 3 32 33 36 33 24 33 33 33 33 18 42 28 42 33 33 33 24 33 33 33 3 3 18 24 3 33 3 33 5 24 3 +Case #292: 6 20 18 18 18 19 1 22 14 18 20 14 3 20 19 18 14 1 11 0 19 6 14 15 6 20 6 +Case #293: 7 6 8 10 8 8 8 0 8 5 +Case #294: 57 11 13 13 14 24 57 14 24 13 13 13 14 0 13 1 57 13 20 24 7 13 7 14 14 13 13 14 13 20 14 13 11 28 20 24 14 13 13 24 14 14 51 13 13 14 13 34 7 16 13 24 14 14 13 24 13 +Case #295: Impossible +Case #296: Impossible +Case #297: 3 3 16 13 14 16 13 3 3 3 16 13 0 3 3 13 +Case #298: 45 0 13 2 45 45 45 45 7 2 45 28 45 13 2 2 7 7 2 45 2 45 2 45 1 2 2 2 2 2 45 1 45 2 45 45 7 45 45 45 45 2 7 25 2 25 +Case #299: 8 3 8 3 10 4 8 0 10 8 +Case #300: 47 19 37 37 47 37 47 19 48 34 27 0 34 19 22 34 27 19 12 48 19 19 41 12 19 2 19 19 27 27 34 6 12 19 34 19 52 32 34 48 47 27 37 32 43 19 34 34 27 39 37 27 27 +Case #301: 0 33 12 12 4 12 12 12 12 33 12 33 1 1 4 1 12 7 12 33 33 1 4 33 4 1 33 12 12 12 12 12 1 12 48 33 12 12 1 4 12 12 48 12 1 4 1 12 12 12 1 1 +Case #302: Impossible +Case #303: Impossible +Case #304: 10 15 28 6 10 28 28 28 20 6 10 7 8 8 28 28 28 6 6 6 7 21 6 8 6 10 28 0 7 22 +Case #305: 20 41 0 3 41 5 34 3 3 3 3 3 41 3 3 3 3 5 3 3 5 5 3 3 5 41 34 3 3 3 3 5 34 5 4 3 3 3 3 3 3 34 34 4 3 3 3 +Case #306: Impossible +Case #307: Impossible +Case #308: 25 0 30 28 8 25 30 17 24 30 30 25 24 30 25 24 25 29 25 24 18 15 30 2 24 24 7 24 24 18 30 30 25 28 2 28 +Case #309: 6 0 7 7 4 4 11 2 4 4 2 4 2 7 2 +Case #310: 13 13 10 10 11 13 13 1 13 13 2 13 0 2 2 1 13 1 2 2 +Case #311: Impossible +Case #312: 47 0 2 8 44 2 53 44 2 41 47 7 2 47 2 8 2 38 8 8 8 8 2 2 41 2 8 7 47 8 2 8 47 2 47 2 2 47 2 2 8 47 2 47 2 44 2 2 47 47 44 2 41 44 2 2 8 47 +Case #313: Impossible +Case #314: Impossible +Case #315: 14 30 0 11 30 22 30 30 13 18 30 30 3 13 13 13 13 13 13 23 23 30 12 13 22 30 22 13 30 13 12 30 +Case #316: 49 11 0 49 3 23 3 3 11 3 4 11 3 3 41 41 3 3 49 49 23 3 49 3 3 3 3 3 3 3 49 4 3 49 3 3 41 3 3 3 49 3 3 3 3 3 2 3 3 3 41 3 2 3 11 3 +Case #317: Impossible +Case #318: 26 12 26 12 21 9 4 9 0 23 9 31 9 9 3 12 14 9 14 9 14 3 3 3 31 21 23 21 25 21 9 3 25 14 14 12 3 31 +Case #319: 0 5 22 1 22 1 8 13 1 5 17 17 1 8 13 13 13 13 22 22 1 1 8 1 17 +Case #320: 52 28 10 28 35 35 35 28 1 33 53 53 35 28 35 28 35 7 8 7 35 53 35 8 35 35 28 7 35 28 35 7 35 53 0 28 7 10 53 28 38 38 35 28 35 38 28 44 38 17 35 33 36 44 35 53 +Case #321: Impossible +Case #322: 27 0 30 29 29 19 17 29 30 29 19 19 29 29 29 27 29 19 29 30 29 29 29 27 30 29 29 29 2 29 +Case #323: Impossible +Case #324: 0 8 1 1 9 8 1 11 1 11 9 9 1 8 1 8 9 +Case #325: 27 27 22 27 22 0 6 6 6 27 22 6 15 22 22 6 6 27 27 22 6 6 27 6 27 6 22 +Case #326: Impossible +Case #327: 2 9 9 2 6 9 8 2 0 +Case #328: Impossible +Case #329: Impossible +Case #330: 4 8 4 7 7 2 0 7 4 +Case #331: 2 0 4 2 2 2 2 1 4 2 1 10 2 4 1 4 4 15 10 4 1 1 4 +Case #332: 43 0 33 19 2 43 2 16 16 2 16 2 43 2 16 6 15 2 43 2 2 27 2 27 16 16 16 16 43 43 43 2 2 2 16 16 2 2 16 2 43 2 33 2 6 16 43 2 2 6 +Case #333: 7 16 11 11 26 15 26 21 7 15 21 15 15 21 7 7 14 20 26 7 1 7 15 3 21 0 +Case #334: Impossible +Case #335: 20 19 20 13 17 0 6 6 13 6 19 20 17 20 6 20 20 17 20 6 6 20 6 6 +Case #336: Impossible +Case #337: 30 27 28 27 32 30 4 21 28 30 8 30 1 1 27 30 28 28 1 30 28 28 30 8 27 27 30 30 27 0 30 27 1 28 +Case #338: Impossible +Case #339: 24 19 19 8 10 19 10 19 19 24 10 17 19 10 13 24 22 19 0 24 19 8 13 19 24 +Case #340: Impossible +Case #341: Impossible +Case #342: 10 12 7 19 0 7 2 10 17 12 17 18 2 4 10 17 19 5 5 2 +Case #343: 45 26 12 26 11 52 11 0 52 8 6 6 11 11 6 52 11 6 11 11 11 52 11 52 11 11 11 6 11 52 11 6 52 6 6 26 11 11 6 52 54 11 26 11 11 6 6 26 6 12 11 8 52 11 11 26 +Case #344: Impossible +Case #345: 4 39 33 11 35 11 33 39 39 36 0 41 39 11 25 39 35 39 11 11 39 25 39 11 11 11 33 41 39 39 36 36 39 33 33 39 11 39 11 11 39 28 33 39 39 39 41 +Case #346: 10 0 2 55 2 2 55 41 41 17 46 2 2 2 2 2 41 2 17 41 2 2 2 55 45 17 55 55 2 2 41 41 2 55 55 41 17 2 55 2 55 46 55 2 17 41 46 55 2 55 2 55 2 55 2 2 2 46 31 +Case #347: 0 1 1 19 1 19 25 1 19 25 1 25 1 25 19 24 19 25 1 25 25 25 1 1 28 1 1 19 1 1 28 25 25 +Case #348: 12 16 12 7 12 12 1 12 16 1 12 0 12 32 43 12 32 1 12 12 43 43 12 16 28 8 16 16 16 12 43 12 12 8 7 32 32 1 12 16 12 1 1 12 +Case #349: 29 21 12 12 31 21 29 12 30 29 29 0 25 12 29 24 21 35 24 31 4 12 4 25 12 21 12 12 21 17 12 29 12 24 4 17 21 29 12 21 25 2 12 24 31 12 12 +Case #350: 10 10 10 10 1 10 10 1 1 0 1 +Case #351: 0 10 14 10 1 13 10 14 13 1 13 13 2 10 +Case #352: Impossible +Case #353: 4 0 43 2 23 19 23 23 35 19 23 19 23 19 2 23 4 23 23 23 2 4 4 23 4 4 23 4 19 23 23 4 23 2 14 23 23 19 35 4 23 23 4 4 2 23 23 19 +Case #354: Impossible +Case #355: 9 30 30 0 9 30 4 9 30 30 30 38 30 18 30 9 15 9 9 30 4 4 30 9 18 30 14 4 18 4 15 9 9 14 9 30 30 30 18 30 +Case #356: 0 1 1 48 1 48 1 1 1 40 48 1 1 1 1 48 1 1 1 48 16 1 1 1 28 1 1 16 1 1 1 1 1 1 48 1 1 53 1 48 1 48 1 48 48 12 48 1 1 1 12 16 1 28 1 1 48 +Case #357: 9 8 8 18 9 8 18 0 8 8 15 8 18 15 8 9 9 2 +Case #358: 9 7 9 3 12 5 3 2 12 12 7 0 1 12 12 +Case #359: 21 12 12 12 48 21 21 22 21 21 48 21 12 24 21 48 21 48 48 12 0 7 8 48 21 48 12 24 21 25 9 22 21 48 21 12 21 8 48 24 7 21 22 9 12 48 12 21 21 +Case #360: 8 6 6 8 7 8 8 0 +Case #361: Impossible +Case #362: Impossible +Case #363: Impossible +Case #364: 0 1 1 1 1 48 1 1 48 1 1 1 59 1 1 1 1 1 1 1 1 1 1 1 6 11 1 1 1 1 1 1 1 1 1 1 1 1 1 6 1 1 1 59 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 +Case #365: Impossible +Case #366: 2 0 1 2 2 1 1 +Case #367: Impossible +Case #368: Impossible +Case #369: Impossible +Case #370: 18 0 2 18 35 8 2 2 50 18 18 18 2 8 2 23 2 2 18 8 8 2 2 2 18 2 2 50 2 2 18 21 4 8 18 18 18 18 4 18 2 8 2 2 2 2 2 2 2 35 18 2 18 2 8 2 18 2 +Case #371: 11 0 13 11 4 13 11 11 11 11 2 2 1 13 11 +Case #372: Impossible +Case #373: Impossible +Case #374: Impossible +Case #375: Impossible +Case #376: 0 1 27 27 1 1 4 27 27 27 27 1 27 1 1 1 27 27 1 27 27 27 1 27 27 1 1 27 1 27 +Case #377: 31 36 31 38 8 31 36 31 31 31 31 24 31 31 24 31 31 31 24 24 0 24 24 21 24 31 36 36 24 31 24 8 31 31 24 29 31 31 31 +Case #378: Impossible +Case #379: Impossible +Case #380: Impossible +Case #381: 4 6 4 0 11 4 6 6 4 11 6 4 11 3 4 4 4 6 4 11 6 4 +Case #382: 48 7 7 38 48 38 38 38 42 19 7 5 19 19 48 19 19 48 0 19 48 38 42 48 42 48 49 26 48 19 38 48 40 26 42 38 19 42 42 38 19 48 19 38 48 19 36 19 38 38 38 49 19 +Case #383: Impossible +Case #384: Impossible +Case #385: 10 12 1 9 10 0 4 10 6 12 7 9 9 +Case #386: 22 11 11 37 23 22 9 22 11 22 22 0 22 22 22 8 11 23 23 22 11 12 11 14 22 11 22 23 37 12 22 22 22 22 11 12 11 +Case #387: 8 8 7 7 14 7 2 16 7 8 14 8 7 3 7 0 +Case #388: 7 11 0 7 7 7 3 19 7 7 17 20 7 7 3 7 7 3 7 7 17 11 19 7 7 3 7 7 7 7 7 7 7 7 11 +Case #389: 47 47 47 20 47 47 0 30 47 7 30 47 47 30 7 47 7 47 7 18 20 47 47 46 47 47 47 30 7 47 47 30 47 30 7 11 47 47 7 47 47 47 47 30 47 7 7 47 47 20 47 +Case #390: 0 1 2 2 2 4 2 1 +Case #391: 4 13 4 0 4 4 42 42 5 4 4 4 4 42 4 4 4 4 4 4 4 4 4 4 4 13 4 4 5 4 4 42 42 4 4 4 4 42 4 42 42 13 4 42 42 13 4 4 4 4 4 26 4 4 5 +Case #392: Impossible +Case #393: 19 28 26 23 15 1 15 15 25 19 26 23 15 1 26 11 26 19 26 26 13 26 28 19 15 0 25 26 15 +Case #394: 0 9 5 5 1 5 6 1 1 +Case #395: 16 35 0 32 16 17 17 50 39 26 41 43 16 43 41 41 16 13 33 16 17 16 16 39 14 16 17 16 41 41 32 33 41 17 33 50 33 16 13 41 3 39 16 33 16 13 16 41 33 33 +Case #396: Impossible +Case #397: 11 11 0 3 3 11 11 22 3 11 3 11 3 11 22 11 3 7 7 11 11 11 3 9 11 +Case #398: 0 14 1 1 1 47 1 47 47 1 14 47 14 47 1 1 1 1 1 1 47 1 1 1 47 47 1 1 1 1 1 47 1 47 47 1 1 1 1 1 1 1 14 1 1 1 1 47 47 1 47 47 1 1 +Case #399: Impossible +Case #400: 26 25 26 20 20 20 26 0 20 26 1 20 20 20 20 26 1 20 14 8 20 19 2 2 26 20 17 1 8 20 26 26 20 +Case #401: Impossible +Case #402: Impossible +Case #403: 3 18 18 9 18 9 32 22 30 22 3 22 20 30 9 22 18 0 9 22 30 3 30 32 22 18 19 18 22 22 32 22 +Case #404: Impossible +Case #405: Impossible +Case #406: 5 1 7 9 6 10 10 7 7 0 4 +Case #407: 31 20 20 31 7 31 31 17 27 33 31 31 4 31 31 21 35 27 35 31 31 31 20 27 31 31 0 7 24 20 35 17 27 21 33 4 +Case #408: 9 32 9 9 34 9 16 9 0 15 16 34 31 16 32 31 9 9 32 16 28 9 16 9 15 9 9 16 16 32 32 9 34 9 16 31 15 +Case #409: Impossible +Case #410: Impossible +Case #411: 11 10 4 12 3 5 3 6 1 3 12 0 3 +Case #412: 24 0 2 2 2 15 32 2 32 2 2 8 31 2 2 15 2 24 44 2 2 2 2 8 2 2 2 8 2 2 2 2 2 2 8 15 44 2 2 31 2 24 2 15 +Case #413: 11 0 2 7 2 11 9 7 2 1 7 6 +Case #414: 0 1 2 1 6 1 +Case #415: Impossible +Case #416: 2 0 2 2 16 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 16 2 2 2 2 2 2 16 24 2 2 2 16 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 24 +Case #417: 7 42 16 16 0 7 5 5 52 16 42 5 16 5 42 1 7 7 5 16 16 42 51 16 42 7 42 27 1 16 5 27 16 27 7 5 16 42 7 52 42 51 7 16 16 16 42 42 16 5 16 51 16 23 42 +Case #418: Impossible +Case #419: 34 13 23 26 0 4 12 26 26 34 26 5 26 26 26 26 26 12 26 5 23 34 34 5 26 12 26 34 26 26 13 26 26 26 5 5 +Case #420: Impossible +Case #421: Impossible +Case #422: 3 16 39 3 3 16 16 34 3 16 34 34 3 39 16 34 3 16 40 16 6 16 16 38 10 39 34 0 21 40 13 39 3 28 3 3 3 13 16 34 3 +Case #423: 0 3 1 5 8 1 6 6 +Case #424: 0 1 1 21 21 21 5 1 21 1 1 21 21 1 16 7 1 1 1 1 1 1 1 +Case #425: Impossible +Case #426: 0 34 1 1 34 17 34 34 34 1 22 1 2 33 8 22 33 34 33 34 17 2 1 22 12 2 8 34 7 1 2 1 2 12 2 34 34 33 34 1 34 34 22 34 7 1 34 2 1 +Case #427: 2 3 0 2 2 +Case #428: Impossible +Case #429: Impossible +Case #430: 11 11 9 3 3 0 3 15 6 3 16 3 11 6 4 3 +Case #431: 13 8 13 13 13 4 29 13 13 0 13 24 24 27 13 27 13 13 24 13 10 14 24 10 13 24 13 10 14 13 +Case #432: 25 25 25 37 25 7 25 33 25 25 37 37 37 25 25 25 25 37 25 37 37 23 37 7 37 25 37 0 2 2 37 10 37 37 37 37 28 25 28 37 25 37 25 +Case #433: 0 21 1 33 21 21 21 21 1 21 21 41 41 21 21 21 41 21 1 41 46 21 1 37 21 21 41 21 21 21 41 21 41 21 1 37 41 21 43 1 21 37 41 21 41 1 21 41 21 33 +Case #434: 35 22 56 0 35 24 24 22 35 4 22 35 4 35 4 4 4 22 4 22 22 35 56 22 35 4 4 4 7 4 4 7 4 4 4 4 7 22 21 21 7 4 4 22 22 35 7 4 4 22 4 22 4 4 4 35 35 +Case #435: Impossible +Case #436: Impossible +Case #437: 13 8 13 7 0 13 8 5 12 8 1 13 8 9 8 +Case #438: 0 4 4 24 4 4 1 4 1 4 4 1 1 1 1 1 1 1 1 5 24 1 1 1 1 +Case #439: Impossible +Case #440: 13 13 16 12 18 5 13 18 12 5 5 13 0 16 12 18 5 13 16 16 12 10 10 12 13 10 10 10 34 28 12 13 26 5 18 13 16 13 5 +Case #441: Impossible +Case #442: Impossible +Case #443: Impossible +Case #444: Impossible +Case #445: 9 0 40 18 40 31 40 40 40 52 31 40 52 40 9 2 52 40 31 31 31 2 40 40 31 9 40 52 2 31 40 40 2 52 18 2 2 40 40 2 52 31 7 2 40 40 2 31 2 40 40 40 +Case #446: Impossible +Case #447: Impossible +Case #448: Impossible +Case #449: 45 33 24 50 32 45 2 50 18 24 33 18 12 24 24 50 24 32 24 24 24 50 32 0 2 24 50 24 45 24 24 50 45 45 24 26 24 24 45 24 24 45 33 24 24 47 2 45 4 45 24 24 33 45 50 53 +Case #450: 6 7 6 8 4 4 8 10 10 0 6 +Case #451: Impossible +Case #452: 2 4 7 7 8 7 0 6 +Case #453: 5 1 1 25 32 32 32 5 32 1 1 1 25 11 1 32 36 20 10 1 32 32 32 32 26 1 20 32 32 1 11 0 20 32 20 10 +Case #454: Impossible +Case #455: Impossible +Case #456: 44 39 39 13 39 39 39 39 39 39 36 17 22 39 39 31 44 0 39 18 13 39 39 13 36 18 39 47 39 39 39 36 17 39 39 39 44 39 18 39 36 44 39 39 13 39 17 39 23 39 +Case #457: Impossible +Case #458: Impossible +Case #459: Impossible +Case #460: 0 1 1 1 11 27 27 1 1 27 1 11 27 27 27 11 1 1 26 11 11 27 1 1 1 27 11 1 1 1 1 27 1 11 27 1 1 11 26 19 1 27 +Case #461: Impossible +Case #462: 30 20 36 27 22 14 27 14 30 14 28 18 0 22 14 27 27 36 28 14 28 28 22 13 30 14 14 13 28 20 30 22 22 28 27 33 22 +Case #463: Impossible +Case #464: 11 11 11 15 11 11 11 11 3 11 0 51 11 15 11 8 3 11 15 11 41 9 11 26 15 15 9 11 11 11 8 15 15 41 19 11 11 41 11 11 9 15 15 3 9 11 11 41 41 15 11 +Case #465: 0 27 27 10 15 26 27 1 27 27 27 10 26 27 26 26 27 10 27 27 10 26 26 27 1 27 1 26 26 1 27 26 1 10 15 1 1 26 26 1 1 10 26 27 26 10 27 27 1 +Case #466: 37 37 12 37 35 4 15 0 35 12 18 8 37 8 12 12 12 12 18 12 12 8 31 15 18 29 18 12 35 12 37 18 12 26 12 29 12 12 12 18 12 12 +Case #467: Impossible +Case #468: Impossible +Case #469: 3 7 7 3 3 7 0 7 +Case #470: Impossible +Case #471: Impossible +Case #472: Impossible +Case #473: 6 6 2 26 2 0 3 2 3 2 3 36 2 2 2 2 29 21 29 3 2 2 29 2 6 2 2 2 6 2 2 2 2 6 6 2 36 3 6 2 2 +Case #474: 15 1 1 1 0 1 14 1 14 5 14 1 1 13 10 14 +Case #475: 6 6 6 3 3 0 6 6 5 5 6 +Case #476: 28 11 1 14 14 1 15 14 0 28 14 1 14 28 1 1 28 15 14 1 14 28 14 14 9 14 28 9 +Case #477: 10 19 29 29 23 10 19 19 8 29 22 0 22 19 19 29 29 19 29 4 19 19 2 19 19 19 29 6 12 19 +Case #478: Impossible +Case #479: Impossible +Case #480: 2 11 6 23 11 7 2 11 7 2 0 2 11 2 23 23 8 16 7 11 10 2 11 25 8 +Case #481: Impossible +Case #482: Impossible +Case #483: Impossible +Case #484: 0 1 48 1 33 1 1 1 1 1 1 1 17 1 1 1 1 1 1 1 1 1 1 33 1 48 37 1 48 1 33 1 1 1 33 1 1 1 33 1 16 48 1 1 1 33 33 1 1 +Case #485: 6 0 2 16 11 30 2 33 32 13 2 2 3 3 30 5 5 3 30 1 5 20 30 5 24 16 30 5 5 16 2 11 20 24 20 +Case #486: 0 30 1 30 1 22 30 30 30 30 30 30 30 30 22 33 30 30 30 30 30 2 30 30 30 18 1 30 18 1 1 30 30 30 30 30 33 +Case #487: 13 0 7 7 13 7 10 13 20 11 2 20 11 5 20 11 11 9 11 6 7 +Case #488: 5 0 8 8 2 31 5 5 8 8 31 2 8 8 2 8 2 5 5 14 14 2 2 31 2 5 2 5 8 2 8 31 5 8 8 8 14 34 2 8 5 14 2 8 2 31 2 21 31 34 2 2 2 8 8 8 2 2 8 +Case #489: 17 0 32 31 32 2 2 16 28 29 16 17 16 16 2 2 28 2 32 2 16 5 5 2 29 16 2 32 32 32 32 16 5 32 5 2 32 31 +Case #490: 27 37 27 13 14 25 52 27 27 27 54 27 37 27 39 51 27 14 27 56 27 56 27 37 37 27 0 37 27 25 14 39 37 51 37 13 27 37 18 56 39 13 27 56 18 18 14 27 18 40 37 39 13 38 27 18 +Case #491: Impossible +Case #492: 10 10 11 14 0 13 3 18 3 13 14 3 3 21 18 11 18 5 14 14 18 +Case #493: 16 28 20 28 28 0 19 6 6 28 20 10 28 28 35 28 6 16 28 16 28 6 28 28 35 28 19 6 28 28 28 28 6 28 16 28 10 37 19 +Case #494: 0 6 7 7 6 1 1 1 4 7 5 +Case #495: 2 0 10 12 14 14 2 2 10 2 12 14 2 2 13 14 +Case #496: 6 25 7 6 6 0 6 21 21 5 9 25 20 6 9 6 21 21 7 7 25 5 7 25 1 +Case #497: 3 1 0 6 1 1 +Case #498: 0 7 2 7 4 5 1 5 11 11 4 4 +Case #499: Impossible +Case #500: Impossible +Case #501: Impossible +Case #502: 8 3 15 8 1 3 3 28 8 6 26 28 3 8 0 28 3 28 8 28 14 6 3 28 6 3 8 3 6 6 6 3 8 28 +Case #503: Impossible +Case #504: Impossible +Case #505: 4 0 6 2 8 9 11 9 2 1 5 +Case #506: 7 9 11 15 6 12 18 3 11 7 7 7 11 15 3 12 18 0 18 +Case #507: Impossible diff --git a/2019/round1/262526658147947.jpg b/2019/round1/262526658147947.jpg new file mode 100644 index 0000000000000000000000000000000000000000..96e9e686284a3950a4c0108f98cf808b412ff371 --- /dev/null +++ b/2019/round1/262526658147947.jpg @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:918081c894c3d2916196c505c30fbec4b90ee770c58a1bda6c4b8aadad167a7f +size 5763 diff --git a/2019/round1/262631865014685.jpg b/2019/round1/262631865014685.jpg new file mode 100644 index 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sha256:fe656b3062f4e23c341ae4ef4f17e1a26ddd2a0f3dfb13291b7b6c7c437d4a49 +size 11935 diff --git a/2019/round1/class_treasurer.cpp b/2019/round1/class_treasurer.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4cdc37fb4cd20fa3bb16cf709f7c9f3c46be82ab --- /dev/null +++ b/2019/round1/class_treasurer.cpp @@ -0,0 +1,130 @@ +// Class Treasurer +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +#define MOD 1000000007 +#define LIM 1000001 + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int N,K; + int i,d,ans; + static char V[LIM]; + static int C[LIM]; + // testcase loop + Read(T); + Fox1(t,T) + { + // input + Read(N),Read(K); + scanf("%s",&V); + // compute costs + Fox(i,N) + C[i]=(i ? C[i-1]*2%MOD : 2); + // greedy + d=ans=0; + FoxR(i,N) + { + if (V[i]=='B') + { + if (d +It's time for your school class to elect its class officers for the year. These officers will have the honour of representing the class and will hold various responsibilities. +The position of class treasurer is particularly appealing to some of the more organized and mathematically-inclined students, especially two rivals, Amy and Betty. +They've both been running strong campaigns, to the point that no other feasible candidates remain. +

+ +

+A democratic vote to elect the class treasurer is about to take place! Each of the N students in the class will cast one vote, for either Amy or Betty. +The students have IDs numbered from 1 to N, and student i is currently planning on voting for either +Amy (if Vi = "A") or Betty (if Vi = "B"). +

+ +

+Your teacher, Mr. X, has some "novel" ideas about how elections should work. Perhaps in an effort to teach your class a statistics lesson, he will organize the election as follows. +He'll consider the set of all N*(N+1)/2 possible non-empty contiguous sets of student IDs, and will select one at random. +Each set will have an equal chance of being selected. He'll refer to this as the "representative set" of students. He will also announce a threshold of victory, K. +He'll then tally up the number of votes for Amy and Betty amongst those students — let these vote counts be a and b respectively. +If a > b + K, then Amy will win. +If b > a + K, then Betty will win. +Otherwise, if |a - b| ≤ K, then it will be a draw (neither candidate will win, and the class will be left without a treasurer). +

+ +

+Amy has grown concerned about how the election will turn out, so she's enlisted your help in potentially swaying some of your classmates' opinions. +She's tasked you with ensuring that, no matter which representative set gets chosen, Betty cannot possibly win (in other words, either Amy will win or neither candidate will win). +To do so, you may pay 0 or more students to change their vote from their current candidate to the other one. +Student i requires 2i dollars to be influenced in this fashion. You must finish paying students off before you know what the representative set will be. +

+ +

+What's the minimum possible cost required to guarantee that Betty cannot possibly win and become the class treasurer? +As this cost may be large, output it modulo 1,000,000,007. +Note that you must minimize the actual cost, rather than minimizing the resulting value of the cost after it's taken modulo 1,000,000,007. +

+ + +

Input

+ +

+Input begins with an integer T, the number of elections. +For each election, there are two lines. The first line contains the space-separated integers N and K. +The second line contains the N characters V1 through VN. +

+ + +

Output

+ +

+For the ith election, print a line containing "Case #i: " +followed by 1 integer, the minimum possible cost (in dollars) required to guarantee that Betty cannot become the class treasurer, modulo 1,000,000,007. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 200
+1 ≤ N ≤ 1,000,000
+0 ≤ KN
+

+ +

Explanation of Sample

+ +

+In the first case, if you do nothing, then Betty may win (if the representative set either consists of only student 1 or only student 4). +You should pay students 1 and 4 to each vote for Amy instead of Betty, for a cost of $2 + $16 = $18. Amy will then be guaranteed to win for any choice of representative set. +

+ +

+In the second case, you don't need to pay any students to change their minds — either Amy will win, or it will be a draw. +

+ +

+In the third case, you should pay student 2 $4 to change their vote to Amy. +

diff --git a/2019/round1/class_treasurer.in b/2019/round1/class_treasurer.in new file mode 100644 index 0000000000000000000000000000000000000000..12f16f5b99e32888c6d4842e83e745ad6e273e91 --- /dev/null +++ b/2019/round1/class_treasurer.in @@ -0,0 +1,621 @@ +310 +4 0 +BAAB +4 1 +BAAB +4 1 +ABBA +5 2 +BBBBB +15 3 +ABBBABBBBBABABB +50 4 +BBABAABBBBABBBBAABBBBAABBBBBABBBAABABBBBBBABABBAAB +1 0 +A +1 0 +B +1 1 +A +1 1 +B +1000000 5000 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the honour of representing the class and will hold +various responsibilities. The position of class treasurer is particularly +appealing to some of the more organized and mathematically-inclined students, +especially two rivals, Amy and Betty. They've both been running strong +campaigns, to the point that no other feasible candidates remain. + +A democratic vote to elect the class treasurer is about to take place! Each of +the **N** students in the class will cast one vote, for either Amy or Betty. +The students have IDs numbered from 1 to **N**, and student _i_ is currently +planning on voting for either Amy (if **Vi** = "A") or Betty (if **Vi** = +"B"). + +Your teacher, Mr. X, has some "novel" ideas about how elections should work. +Perhaps in an effort to teach your class a statistics lesson, he will organize +the election as follows. He'll consider the set of all **N***(**N**+1)/2 +possible non-empty contiguous sets of student IDs, and will select one at +random. Each set will have an equal chance of being selected. He'll refer to +this as the "representative set" of students. He will also announce a +threshold of victory, **K**. He'll then tally up the number of votes for Amy +and Betty amongst those students — let these vote counts be **a** and **b** +respectively. If **a** > **b** \+ **K**, then Amy will win. If **b** > **a** +\+ **K**, then Betty will win. Otherwise, if |**a** \- **b**| ≤ **K**, then it +will be a draw (neither candidate will win, and the class will be left without +a treasurer). + +Amy has grown concerned about how the election will turn out, so she's +enlisted your help in potentially swaying some of your classmates' opinions. +She's tasked you with ensuring that, no matter which representative set gets +chosen, Betty cannot possibly win (in other words, either Amy will win or +neither candidate will win). To do so, you may pay 0 or more students to +change their vote from their current candidate to the other one. Student _i_ +requires 2i dollars to be influenced in this fashion. You must finish paying +students off _before_ you know what the representative set will be. + +What's the minimum possible cost required to guarantee that Betty cannot +possibly win and become the class treasurer? As this cost may be large, output +it modulo 1,000,000,007. Note that you must minimize the actual cost, rather +than minimizing the resulting value of the cost after it's taken modulo +1,000,000,007. + +### Input + +Input begins with an integer **T**, the number of elections. For each +election, there are two lines. The first line contains the space-separated +integers **N** and **K**. The second line contains the **N** characters **V1** +through **VN**. + +### Output + +For the _i_th election, print a line containing "Case #_i_: " followed by 1 +integer, the minimum possible cost (in dollars) required to guarantee that +Betty cannot become the class treasurer, modulo 1,000,000,007. + +### Constraints + +1 ≤ **T** ≤ 200 +1 ≤ **N** ≤ 1,000,000 +0 ≤ **K** ≤ **N** + +### Explanation of Sample + +In the first case, if you do nothing, then Betty may win (if the +representative set either consists of only student 1 or only student 4). You +should pay students 1 and 4 to each vote for Amy instead of Betty, for a cost +of $2 + $16 = $18. Amy will then be guaranteed to win for any choice of +representative set. + +In the second case, you don't need to pay any students to change their minds — +either Amy will win, or it will be a draw. + +In the third case, you should pay student 2 $4 to change their vote to Amy. + diff --git a/2019/round1/class_treasurer.out b/2019/round1/class_treasurer.out new file mode 100644 index 0000000000000000000000000000000000000000..ef333d75ec690effeda17552df6b0dc93f2f1ce9 --- /dev/null +++ b/2019/round1/class_treasurer.out @@ -0,0 +1,310 @@ +Case #1: 18 +Case #2: 0 +Case #3: 4 +Case #4: 10 +Case #5: 324 +Case #6: 363067831 +Case #7: 0 +Case #8: 2 +Case #9: 0 +Case #10: 0 +Case #11: 3915602 +Case #12: 420527559 +Case #13: 373596085 +Case #14: 797276543 +Case #15: 408712914 +Case #16: 0 +Case #17: 176056122 +Case #18: 227768764 +Case #19: 860083851 +Case #20: 0 +Case #21: 619120623 +Case #22: 412574133 +Case #23: 0 +Case #24: 38294913 +Case #25: 690346 +Case #26: 441205616 +Case #27: 0 +Case #28: 231175780 +Case #29: 0 +Case #30: 0 +Case #31: 0 +Case #32: 35971959 +Case #33: 0 +Case #34: 785156710 +Case #35: 0 +Case #36: 0 +Case #37: 0 +Case #38: 972522494 +Case #39: 976105974 +Case #40: 0 +Case #41: 0 +Case #42: 0 +Case #43: 478469427 +Case #44: 0 +Case #45: 0 +Case #46: 0 +Case #47: 0 +Case #48: 285613897 +Case #49: 0 +Case #50: 243203813 +Case #51: 511914854 +Case #52: 0 +Case #53: 818735744 +Case #54: 471900416 +Case #55: 985363238 +Case #56: 0 +Case #57: 0 +Case #58: 483650993 +Case #59: 584263749 +Case #60: 267584 +Case #61: 0 +Case #62: 0 +Case #63: 840962697 +Case #64: 411456125 +Case #65: 0 +Case #66: 34643487 +Case #67: 295192609 +Case #68: 226059585 +Case #69: 575621618 +Case #70: 0 +Case #71: 0 +Case #72: 27500266 +Case #73: 854222438 +Case #74: 772479334 +Case #75: 0 +Case #76: 314790007 +Case #77: 0 +Case #78: 0 +Case #79: 0 +Case #80: 0 +Case #81: 852552226 +Case #82: 119576189 +Case #83: 112779404 +Case #84: 689137954 +Case #85: 523615014 +Case #86: 0 +Case #87: 0 +Case #88: 0 +Case #89: 959478675 +Case #90: 161455788 +Case #91: 27763268 +Case #92: 0 +Case #93: 978354013 +Case #94: 558538736 +Case #95: 0 +Case #96: 134724422 +Case #97: 0 +Case #98: 0 +Case #99: 0 +Case #100: 0 +Case #101: 95512563 +Case #102: 6654 +Case #103: 0 +Case #104: 0 +Case #105: 810157525 +Case #106: 0 +Case #107: 264419113 +Case #108: 0 +Case #109: 639539945 +Case #110: 623554504 +Case #111: 268331719 +Case #112: 153450517 +Case #113: 0 +Case #114: 0 +Case #115: 0 +Case #116: 697628936 +Case #117: 0 +Case #118: 0 +Case #119: 714883891 +Case #120: 0 +Case #121: 814123718 +Case #122: 738072225 +Case #123: 124901202 +Case #124: 0 +Case #125: 0 +Case #126: 0 +Case #127: 0 +Case #128: 0 +Case #129: 504919248 +Case #130: 835231303 +Case #131: 698997489 +Case #132: 0 +Case #133: 0 +Case #134: 0 +Case #135: 370851409 +Case #136: 569256148 +Case #137: 0 +Case #138: 0 +Case #139: 239033191 +Case #140: 0 +Case #141: 0 +Case #142: 896863209 +Case #143: 364309091 +Case #144: 0 +Case #145: 0 +Case #146: 24809584 +Case #147: 219510325 +Case #148: 0 +Case #149: 0 +Case #150: 766840172 +Case #151: 0 +Case #152: 0 +Case #153: 52819878 +Case #154: 0 +Case #155: 0 +Case #156: 0 +Case #157: 0 +Case #158: 508982928 +Case #159: 311533814 +Case #160: 0 +Case #161: 698519423 +Case #162: 667689114 +Case #163: 178571565 +Case #164: 0 +Case #165: 0 +Case #166: 0 +Case #167: 0 +Case #168: 737278398 +Case #169: 0 +Case #170: 267841120 +Case #171: 207772639 +Case #172: 0 +Case #173: 179716446 +Case #174: 0 +Case #175: 0 +Case #176: 0 +Case #177: 798952787 +Case #178: 64185742 +Case #179: 4 +Case #180: 651222874 +Case #181: 533940195 +Case #182: 0 +Case #183: 0 +Case #184: 498573453 +Case #185: 294967268 +Case #186: 0 +Case #187: 1049120 +Case #188: 0 +Case #189: 0 +Case #190: 646877478 +Case #191: 315816649 +Case #192: 400803684 +Case #193: 183084126 +Case #194: 0 +Case #195: 0 +Case #196: 818558768 +Case #197: 0 +Case #198: 494092823 +Case #199: 0 +Case #200: 946201000 +Case #201: 0 +Case #202: 0 +Case #203: 651767076 +Case #204: 0 +Case #205: 220066174 +Case #206: 0 +Case #207: 0 +Case #208: 874487689 +Case #209: 0 +Case #210: 20834959 +Case #211: 0 +Case #212: 0 +Case #213: 838001850 +Case #214: 0 +Case #215: 70461558 +Case #216: 0 +Case #217: 899346365 +Case #218: 0 +Case #219: 0 +Case #220: 0 +Case #221: 0 +Case #222: 925650463 +Case #223: 178659987 +Case #224: 0 +Case #225: 528631139 +Case #226: 129922549 +Case #227: 784979581 +Case #228: 0 +Case #229: 0 +Case #230: 472506945 +Case #231: 298058006 +Case #232: 576896108 +Case #233: 200374200 +Case #234: 259402088 +Case #235: 0 +Case #236: 0 +Case #237: 143305354 +Case #238: 0 +Case #239: 366964526 +Case #240: 835370798 +Case #241: 0 +Case #242: 0 +Case #243: 0 +Case #244: 0 +Case #245: 0 +Case #246: 0 +Case #247: 0 +Case #248: 574950657 +Case #249: 756486 +Case #250: 536977740 +Case #251: 0 +Case #252: 0 +Case #253: 0 +Case #254: 0 +Case #255: 0 +Case #256: 0 +Case #257: 0 +Case #258: 0 +Case #259: 0 +Case #260: 0 +Case #261: 535192113 +Case #262: 0 +Case #263: 0 +Case #264: 0 +Case #265: 0 +Case #266: 0 +Case #267: 480373327 +Case #268: 687709112 +Case #269: 0 +Case #270: 498776773 +Case #271: 546435991 +Case #272: 0 +Case #273: 0 +Case #274: 0 +Case #275: 0 +Case #276: 0 +Case #277: 127790474 +Case #278: 0 +Case #279: 2012 +Case #280: 172637382 +Case #281: 143996019 +Case #282: 0 +Case #283: 922665672 +Case #284: 0 +Case #285: 557545755 +Case #286: 81907108 +Case #287: 794116416 +Case #288: 519555860 +Case #289: 483749155 +Case #290: 930411527 +Case #291: 290967149 +Case #292: 0 +Case #293: 184 +Case #294: 0 +Case #295: 828789260 +Case #296: 850065568 +Case #297: 874982602 +Case #298: 215459198 +Case #299: 666541384 +Case #300: 346169693 +Case #301: 941909325 +Case #302: 0 +Case #303: 0 +Case #304: 0 +Case #305: 348672159 +Case #306: 325376954 +Case #307: 0 +Case #308: 29441614 +Case #309: 715775417 +Case #310: 832 diff --git a/2019/round1/connect_the_dots.cpp b/2019/round1/connect_the_dots.cpp new file mode 100644 index 0000000000000000000000000000000000000000..73d78df88a95686a0a317e7a0b42ded3b4d9d3dd --- /dev/null +++ b/2019/round1/connect_the_dots.cpp @@ -0,0 +1,158 @@ +// Connect the Dots +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +#define LIM 800001 + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int N,H,V; + int i,j,si,a,b,c,d; + static int G[2][LIM]; + static PR P[LIM]; + static int maxY[LIM]; + set S; + set::iterator I; + // testcase loop + Read(T); + Fox1(t,T) + { + // input, and generate coordinates + Read(N),Read(H),Read(V); + Fox(i,2) + { + Read(G[i][0]),Read(G[i][1]),Read(a),Read(b),Read(c),Read(d); + FoxI(j,2,N-1) + G[i][j]=((LL)a*G[i][j-2] + (LL)b*G[i][j-1] + c)%d+1; + } + // impossible? + int ans=-1; + if (H+VV) + continue; + // g of the dots so far must also use vert. segments + int g=max(0,min(N-H,V)-f); + while (si>g) + I--,si--; + while (six,maxY[i])); + } + // output +Done:; + printf("Case #%d: %d\n",t,ans); + } + return(0); +} \ No newline at end of file diff --git a/2019/round1/connect_the_dots.html b/2019/round1/connect_the_dots.html new file mode 100644 index 0000000000000000000000000000000000000000..f63d34a0b0d29fb04fe055701b624ef09a84bd17 --- /dev/null +++ b/2019/round1/connect_the_dots.html @@ -0,0 +1,121 @@ +

+There are N dots on a 2D grid, the ith of which is a point at coordinates (Xi, Yi). +All coordinates are positive integers, and all N dots' positions are distinct. +

+ +

+You'd like to draw N line segments, each of which is either horizontal or vertical, to "connect" each of the dots to one of the grid's axes. +In particular, for each dot i, you'll draw either a horizontal line segment connecting it to the y-axis +(with endpoints (0, Yi) and (Xi, Yi)), +or a vertical line segment connecting it to the x-axis (with endpoints (Xi, 0) and (Xi, Yi)). +Each line segment only counts as "connecting" the single dot located at its endpoint, even if it happens to pass through other dots along the way. +

+ +

+No horizontal line segment is allowed to intersect with any vertical line segment. Line segments are not considered to intersect at either of their endpoints — +for example, it's permitted for a horizontal line segment to pass through the endpoint of a vertical one, or vice versa. +Horizontal line segments are allowed to overlap with other horizontal ones, as are vertical line segments with other vertical ones. +

+ +

+The cost of drawing a non-empty set of horizontal line segments is equal to the length of the longest one (in dollars), while the cost of drawing no horizontal line segments is $0. +The cost of drawing a set of vertical line segments is similarly equal to the length of the longest one (if any), +and the total cost of drawing all N line segments is equal to the cost of drawing the set of horizontal ones plus the cost of drawing the set of vertical ones. +

+ +

+You can choose to draw at most H horizontal line segments, and at most V vertical ones. +What's the minimum total cost required to connect all N dots to the grid's axes, +without using too many of either type of line segment or causing any horizontal line segments to intersect with vertical ones, if that can be done at all? +

+ +

+In order to reduce the size of the input, the dots' coordinates will not all be provided explicitly. Instead, you'll be given +X1, X2, Y1, Y2, as well as 8 constants +Ax, Bx, Cx, Dx, +Ay, By, Cy, and Dy, +and you must then compute X3..N and Y3..N +as follows (bearing in mind that intermediate values may not fit within 32-bit integers): +

+ +

+Xi = +((Ax * Xi-2 + +Bx * Xi-1 + +Cx) modulo Dx) + 1, for i = 3..N +

+ +

+Yi = +((Ay * Yi-2 + +By * Yi-1 + +Cy) modulo Dy) + 1, for i = 3..N +

+ + +

Input

+ +

+Input begins with an integer T, the number of grids. +For each room, there are three lines. +The first line contains the space-separated integers N, H, and V. +The second line contains the space-separated integers +X1, X2, +Ax, Bx, Cx, and Dx. +The third line contains the space-separated integers +Y1, Y2, +Ay, By, Cy, and Dy. +

+ + +

Output

+ +

+For the ith grid, print a line containing "Case #i: " +followed by the minimum total cost (in dollars) required to validly connect all N dots to the grid's axes, or -1 if it's impossible to do so. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 160
+2 ≤ N ≤ 800,000
+0 ≤ H, VN
+0 ≤ Ax, Bx, Cx +Ay, By, Cy ≤ 1,000,000,000
+1 ≤ Dx, Dy ≤ 1,000,000,000
+1 ≤ XiDx
+1 ≤ YiDy
+

+ +

+In the first case, the dots are at coordinates (6, 2) and (3, 4). The cheapest option is to connect both dots using vertical line segments, having lengths 2 and 4 and altogether costing $4 to draw. +The lack of horizontal line segments costs an additional $0, bringing the total to $4 + $0 = $4. +

+ + + +

+The second case is the same as the first, except that at most one vertical line may be drawn. +The cheapest valid option is now to connect the second dot using a horizontal line segment (of length 3) while still connecting the first dot using a vertical one (of length 2). +These two line segments do not intersect, and cost a total of $3 + $2 = $5 to draw. +

+ + + +

+In the third case, not all of the dots can be connected. +

+ +

+In the fourth case, the dots are at coordinates (1, 1), (1, 2), (2, 1), and (2, 2). +You can connect the first dot using a horizontal line segment (of length 1), and the other dots with vertical ones (of lengths at most 2), for a total cost of $1 + $2 = $3. +Note that this causes two vertical line segments to overlap (the ones connecting the third and fourth points). +

+ + + +

+In the fifth case, the dots are at coordinates (15, 34), (19, 3), (2, 38), (13, 17), (18, 14), (25, 15), (42, 18), (9, 11), (26, 34), and (41, 19). +

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b/2019/round1/connect_the_dots.md new file mode 100644 index 0000000000000000000000000000000000000000..b59803b9542e1085d2ca6c715aaed63ecfdbf13b --- /dev/null +++ b/2019/round1/connect_the_dots.md @@ -0,0 +1,97 @@ +There are **N** dots on a 2D grid, the _i_th of which is a point at +coordinates (**Xi**, **Yi**). All coordinates are positive integers, and all +**N** dots' positions are distinct. + +You'd like to draw **N** line segments, each of which is either horizontal or +vertical, to "connect" each of the dots to one of the grid's axes. In +particular, for each dot _i_, you'll draw either a horizontal line segment +connecting it to the y-axis (with endpoints (0, **Yi**) and (**Xi**, **Yi**)), +or a vertical line segment connecting it to the x-axis (with endpoints +(**Xi**, 0) and (**Xi**, **Yi**)). Each line segment only counts as +"connecting" the single dot located at its endpoint, even if it happens to +pass through other dots along the way. + +No horizontal line segment is allowed to intersect with any vertical line +segment. Line segments are **not** considered to intersect at either of their +endpoints — for example, it's permitted for a horizontal line segment to pass +through the endpoint of a vertical one, or vice versa. Horizontal line +segments are allowed to overlap with other horizontal ones, as are vertical +line segments with other vertical ones. + +The cost of drawing a non-empty set of horizontal line segments is equal to +the length of the longest one (in dollars), while the cost of drawing no +horizontal line segments is $0. The cost of drawing a set of vertical line +segments is similarly equal to the length of the longest one (if any), and the +total cost of drawing all **N** line segments is equal to the cost of drawing +the set of horizontal ones plus the cost of drawing the set of vertical ones. + +You can choose to draw at most **H** horizontal line segments, and at most +**V** vertical ones. What's the minimum total cost required to connect all +**N** dots to the grid's axes, without using too many of either type of line +segment or causing any horizontal line segments to intersect with vertical +ones, if that can be done at all? + +In order to reduce the size of the input, the dots' coordinates will not all +be provided explicitly. Instead, you'll be given **X1**, **X2**, **Y1**, +**Y2**, as well as 8 constants **Ax**, **Bx**, **Cx**, **Dx**, **Ay**, **By**, +**Cy**, and **Dy**, and you must then compute **X3..N** and **Y3..N** as +follows (bearing in mind that intermediate values may not fit within 32-bit +integers): + +**Xi** = ((**Ax** * **Xi-2** \+ **Bx** * **Xi-1** \+ **Cx**) modulo **Dx**) + 1, for _i_ = 3..**N** + +**Yi** = ((**Ay** * **Yi-2** \+ **By** * **Yi-1** \+ **Cy**) modulo **Dy**) + 1, for _i_ = 3..**N** + +### Input + +Input begins with an integer **T**, the number of grids. For each room, there +are three lines. The first line contains the space-separated integers **N**, +**H**, and **V**. The second line contains the space-separated integers +**X1**, **X2**, **Ax**, **Bx**, **Cx**, and **Dx**. The third line contains +the space-separated integers **Y1**, **Y2**, **Ay**, **By**, **Cy**, and +**Dy**. + +### Output + +For the _i_th grid, print a line containing "Case #_i_: " followed by the +minimum total cost (in dollars) required to validly connect all **N** dots to +the grid's axes, or -1 if it's impossible to do so. + +### Constraints + +1 ≤ **T** ≤ 160 +2 ≤ **N** ≤ 800,000 +0 ≤ **H**, **V** ≤ **N** +0 ≤ **Ax**, **Bx**, **Cx** **Ay**, **By**, **Cy** ≤ 1,000,000,000 +1 ≤ **Dx**, **Dy** ≤ 1,000,000,000 +1 ≤ **Xi** ≤ **Dx** +1 ≤ **Yi** ≤ **Dy** + +In the first case, the dots are at coordinates (6, 2) and (3, 4). The cheapest +option is to connect both dots using vertical line segments, having lengths 2 +and 4 and altogether costing $4 to draw. The lack of horizontal line segments +costs an additional $0, bringing the total to $4 + $0 = $4. + +![]({{PHOTO_ID:282249922896220}}) + +The second case is the same as the first, except that at most one vertical +line may be drawn. The cheapest valid option is now to connect the second dot +using a horizontal line segment (of length 3) while still connecting the first +dot using a vertical one (of length 2). These two line segments do not +intersect, and cost a total of $3 + $2 = $5 to draw. + +![]({{PHOTO_ID:292271182178799}}) + +In the third case, not all of the dots can be connected. + +In the fourth case, the dots are at coordinates (1, 1), (1, 2), (2, 1), and +(2, 2). You can connect the first dot using a horizontal line segment (of +length 1), and the other dots with vertical ones (of lengths at most 2), for a +total cost of $1 + $2 = $3. Note that this causes two vertical line segments +to overlap (the ones connecting the third and fourth points). + +![]({{PHOTO_ID:262631865014685}}) + +In the fifth case, the dots are at coordinates (15, 34), (19, 3), (2, 38), +(13, 17), (18, 14), (25, 15), (42, 18), (9, 11), (26, 34), and (41, 19). + diff --git a/2019/round1/connect_the_dots.out b/2019/round1/connect_the_dots.out new file mode 100644 index 0000000000000000000000000000000000000000..15ae274a253bbf17fdedc3f8cc9e631959bfe584 --- /dev/null +++ b/2019/round1/connect_the_dots.out @@ -0,0 +1,1018 @@ +Case #1: 4 +Case #2: 5 +Case #3: -1 +Case #4: 3 +Case #5: 45 +Case #6: 766791757 +Case #7: 574065510 +Case #8: 329717557 +Case #9: 184312132 +Case #10: 97647486 +Case #11: 534877748 +Case #12: 414517067 +Case #13: 134974209 +Case #14: 766791757 +Case #15: 1000000000 +Case #16: 1999200001 +Case #17: 1999200001 +Case #18: 1999999999 +Case #19: 932357797 +Case #20: 286028535 +Case #21: 795154737 +Case #22: 738895152 +Case #23: 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273677891 +Case #996: 289112690 +Case #997: 340816129 +Case #998: 687448941 +Case #999: 287434997 +Case #1000: 274461130 +Case #1001: 373754629 +Case #1002: 161554099 +Case #1003: 789333552 +Case #1004: 293136973 +Case #1005: 573005690 +Case #1006: 600509664 +Case #1007: 973561922 +Case #1008: 152533151 +Case #1009: 661412320 +Case #1010: 290871537 +Case #1011: 786655959 +Case #1012: -1 +Case #1013: 1025867441 +Case #1014: 159311760 +Case #1015: 467424299 +Case #1016: 155315473 +Case #1017: -1 +Case #1018: 212861756 diff --git a/2019/round1/graphs_as_a_service.cpp b/2019/round1/graphs_as_a_service.cpp new file mode 100644 index 0000000000000000000000000000000000000000..4d62727df408e1bbd42547f35e9bddaef8c2e9a9 --- /dev/null +++ b/2019/round1/graphs_as_a_service.cpp @@ -0,0 +1,130 @@ +// Graphs as a Service +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int N,M; + int i,j,k; + int X[1000],Y[1000],Z[1000]; + int dist[50][50]; + // testcase loop + Read(T); + Fox1(t,T) + { + // init + Fill(dist,60); + // input + Read(N),Read(M); + Fox(i,M) + { + Read(X[i]),Read(Y[i]),Read(Z[i]),X[i]--,Y[i]--; + dist[X[i]][Y[i]]=dist[Y[i]][X[i]]=Z[i]; + } + // Floyd's + Fox(i,N) + Fox(j,N) + Fox(k,N) + Min(dist[j][k],dist[j][i]+dist[i][k]); + // check validity, and output + printf("Case #%d: ",t); + Fox(i,M) + if (dist[X[i]][Y[i]]!=Z[i]) + { + printf("Impossible\n"); + goto Done; + } + printf("%d\n",M); + Fox(i,M) + printf("%d %d %d\n",X[i]+1,Y[i]+1,Z[i]); +Done:; + } + return(0); +} \ No newline at end of file diff --git a/2019/round1/graphs_as_a_service.html b/2019/round1/graphs_as_a_service.html new file mode 100644 index 0000000000000000000000000000000000000000..544f903d9b787a9ef1cd27f6267e51db68f4551b --- /dev/null +++ b/2019/round1/graphs_as_a_service.html @@ -0,0 +1,86 @@ +

+With a successful commission under his belt, Carlos has really made a splash +with his consulting firm, Carlos Structures Industries. His next customer is +Texas Instruments, the well-known manufacturer of graphing calculators. +

+ +

+ +"In today's competitive environment, you need an edge. I can make sure that +your newest graphing calculator is chock-full of the best modern graphs." + +

+ +

+Carlos's pitch seems to have worked as Texas Instruments has ordered an +undirected, weighted graph. Their R&D department has come up with a list +of requirements that will ensure the graph is a hit with Gen Z schoolchildren. +

+ +

+To start with, the graph must have N nodes numbered 1 to N. It must have no +self-loops and at most one edge connecting each unordered pair of nodes. The +weight of each edge must be an integer between 1 and 1,000,000, inclusive. +The graph does not need to be connected. +

+ +

+The graph must also satisfy M customer requirements, the ith of which states +that the shortest distance between two different nodes Xi and Yi must be equal to Zi. +No two requirements pertain to the same unordered pair of nodes. +

+ +

+Carlos's goal is to find any valid graph consistent with all of these requirements +if possible, or to determine that no such graph exists. +

+ + + +

Input

+ +

+Input begins with an integer T, the number of graphs that Texas Instruments has commissioned. +For each graph, there is first a line containing the space-separated integers N and M. +Then, M lines follow, the ith of which contains the space-separated integers +Xi, Yi, and Zi. +

+ + +

Output

+ +

+For the ith graph, print a line containing "Case #i: " +followed by either an integer E and then a description of a valid graph if possible, or the string "Impossible" if no valid graph exists. +

+ +

+A graph description contains E lines, where E is the number of edges in your graph. +The ith line contains the space-separated integers +Ai, Bi, and Wi +indicating that there is an edge between nodes Ai and Bi with weight Wi. +Please keep in mind that your graph must satisfy all of the requirements stated above (both the fundamental requirements dictated by Texas Instruments, and the M customer ones). +

+ + +

Constraints

+ +

+1 ≤ T ≤ 350
+2 ≤ N ≤ 50
+1 ≤ M ≤ 1,000
+1 ≤ Xi, YiN
+XiYi
+1 ≤ Zi ≤ 1,000,000
+

+ +

Explanation of Sample

+ +

+In the graph described by the first sample case's sample output, the shortest distance between nodes 3 and 1 is 5 (along the path 3 -> 2 -> 1), as required. Multiple other outputs would also be accepted for this case. +

+ +

+Multiple other outputs would also be accepted for the third and fourth cases. +

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a/2019/round1/graphs_as_a_service.md b/2019/round1/graphs_as_a_service.md new file mode 100644 index 0000000000000000000000000000000000000000..f98eaf88645a6810a6b1fd1d7392fb19a4b08d19 --- /dev/null +++ b/2019/round1/graphs_as_a_service.md @@ -0,0 +1,62 @@ +With a successful commission under his belt, Carlos has really made a splash +with his consulting firm, Carlos Structures Industries. His next customer is +Texas Instruments, the well-known manufacturer of graphing calculators. + +_ "In today's competitive environment, you need an edge. I can make sure that +your newest graphing calculator is chock-full of the best modern graphs." _ + +Carlos's pitch seems to have worked as Texas Instruments has ordered an +undirected, weighted graph. Their R&D department has come up with a list of +requirements that will ensure the graph is a hit with Gen Z schoolchildren. + +To start with, the graph must have **N** nodes numbered 1 to **N**. It must +have no self-loops and at most one edge connecting each unordered pair of +nodes. The weight of each edge must be an integer between 1 and 1,000,000, +inclusive. The graph does not need to be connected. + +The graph must also satisfy **M** customer requirements, the _i_th of which +states that the shortest distance between two different nodes **Xi** and +**Yi** must be equal to **Zi**. No two requirements pertain to the same +unordered pair of nodes. + +Carlos's goal is to find any valid graph consistent with all of these +requirements if possible, or to determine that no such graph exists. + +### Input + +Input begins with an integer **T**, the number of graphs that Texas +Instruments has commissioned. For each graph, there is first a line containing +the space-separated integers **N** and **M**. Then, **M** lines follow, the +_i_th of which contains the space-separated integers **Xi**, **Yi**, and +**Zi**. + +### Output + +For the _i_th graph, print a line containing "Case #_i_: " followed by either +an integer **E** and then a description of a valid graph if possible, or the +string "Impossible" if no valid graph exists. + +A graph description contains **E** lines, where **E** is the number of edges +in your graph. The _i_th line contains the space-separated integers **Ai**, +**Bi**, and **Wi** indicating that there is an edge between nodes **Ai** and +**Bi** with weight **Wi**. Please keep in mind that your graph must satisfy +all of the requirements stated above (both the fundamental requirements +dictated by Texas Instruments, and the **M** customer ones). + +### Constraints + +1 ≤ **T** ≤ 350 +2 ≤ **N** ≤ 50 +1 ≤ **M** ≤ 1,000 +1 ≤ **Xi**, **Yi** ≤ **N** +**Xi** ≠ **Yi** +1 ≤ **Zi** ≤ 1,000,000 + +### Explanation of Sample + +In the graph described by the first sample case's sample output, the shortest +distance between nodes 3 and 1 is 5 (along the path 3 -> 2 -> 1), as required. +**Multiple other outputs would also be accepted for this case.** + +**Multiple other outputs would also be accepted for the third and fourth cases.** + diff --git a/2019/round1/graphs_as_a_service.out b/2019/round1/graphs_as_a_service.out new file mode 100644 index 0000000000000000000000000000000000000000..97849e064364b608603f53f51b91fbb702ab5bfe --- /dev/null +++ b/2019/round1/graphs_as_a_service.out @@ -0,0 +1,67578 @@ +Case #1: 1 +3 1 5 +Case #2: Impossible +Case #3: 3 +1 4 5 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0000000000000000000000000000000000000000..9940035a4de642b6f0a2ac240bad8ceeb384cc11 --- /dev/null +++ b/2019/round1/ladders_and_snakes.cpp @@ -0,0 +1,207 @@ +// Ladders and Snakes +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +#define LIM 50 + +struct Dinic { + struct Edge { + int to, rev, c, f; + Edge(int to, int rev, int c, int f) : to(to), rev(rev), c(c), f(f) {} + }; + vector lvl, ptr, q; + vector< vector > adj; + + Dinic(int n) : lvl(n), ptr(n), q(n), adj(n) {} + + void addEdge(int a, int b, int c) { + adj[a].pb(Edge(b, Sz(adj[b]), c, 0)); + adj[b].pb(Edge(a, Sz(adj[a]) - 1, 0, 0)); + } + + int dfs(int v, int t, int f) { + if (v == t || !f) return f; + for (int& i = ptr[v]; i < Sz(adj[v]); i++) { + Edge& e = adj[v][i]; + if (lvl[e.to] == lvl[v] + 1) { + if (int p = dfs(e.to, t, min(f, e.c - e.f))) { + e.f += p, adj[e.to][e.rev].f -= p; + return p; + } + } + } + return 0; + } + + int calc(int s, int t) { + int L, flow = 0; q[0] = s; + Fox(L,31) { + do { + lvl = ptr = vector(Sz(q)); + int qi = 0, qe = lvl[s] = 1; + while (qi < qe && !lvl[t]) { + int i, v = q[qi++]; + Fox(i,Sz(adj[v])) { + Edge e=adj[v][i]; + if (!lvl[e.to] && (e.c - e.f) >> (30 - L)) { + q[qe++] = e.to, lvl[e.to] = lvl[v] + 1; + } + } + } + while (int p = dfs(s, t, INF)) flow += p; + } while (lvl[t]); + } + return flow; + } +}; + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int N,H; + int i,j,k; + int X[LIM],A[LIM],B[LIM]; + // testcase loop + Read(T); + Fox1(t,T) + { + // input + Read(N),Read(H); + Fox(i,N) + Read(X[i]),Read(A[i]),Read(B[i]); + // construct flow graph + Dinic D(N+2); + Fox(i,N) + { + // connected to bottom? + if (A[i]==0) + D.addEdge(N,i,1e7); + // connected to top? + if (B[i]==H) + D.addEdge(i,N+1,1e7); + // consider connections to other ladders + Fox(j,N) + if (X[i] > E; + Fox(k,N) + if ((X[i]<=X[k]) && (X[k]<=X[j])) + { + E.pb(mp(A[k],mp(1,k))); + E.pb(mp(B[k],mp(0,k))); + } + int s=0; + set S; + sort(All(E)); + Fox(k,Sz(E)) + { + if (E[k].y.x) + S.insert(E[k].y.y); + else + S.erase(E[k].y.y); + if ((Sz(S)==2) && (S.count(i)) && (S.count(j))) + s+=E[k+1].x-E[k].x; + } + if (s) + { + D.addEdge(i,j,s); + D.addEdge(j,i,s); + } + } + } + // compute min cut + int ans=D.calc(N,N+1); + if (ans>=1e7) + ans=-1; + // output + printf("Case #%d: %d\n",t,ans); + } + return(0); +} \ No newline at end of file diff --git a/2019/round1/ladders_and_snakes.html b/2019/round1/ladders_and_snakes.html new file mode 100644 index 0000000000000000000000000000000000000000..46a26ebfcd1fe526299edcbf2b89be78539e0d87 --- /dev/null +++ b/2019/round1/ladders_and_snakes.html @@ -0,0 +1,81 @@ +

+N ladders have been set up in a room, which can be represented as a 2D plane when viewed from the side. +The room's floor is the horizontal line with y-coordinate 0, and its ceiling is the horizontal line with y-coordinate H. +The ith ladder is a vertical line segment between integral coordinates +(Xi, Ai) and (Xi, Bi), located within the inclusive bounds of the room +(such that 0 ≤ Ai < BiH). +Note that each ladder may be touching the floor and/or ceiling, or may be floating in mid-air (don't question it). No two ladders overlap with one another (even at their endpoints). +

+ +

+Sneider the Snake has taken an interest in this room, and may add 0 or more snakes to it. The jth snake will be a vertical line segment between some coordinates +(xj, aj) and (xj, bj), located strictly inside the bounds of the room +(with xj being any non-negative real number, and aj and bj being integers such that +0 < ajbj < H). +A snake may be a length-0 line segment, with its endpoints being equal, in which case it occupies only a single point on the plane. +No snake may overlap with any other snake, nor with any ladder (even at an endpoint). +

+ +

+Flynn the Flying Squirrel finds herself on the floor at coordinates (0, 0), and wants to reach coordinates (0, H) on the ceiling. +At any point, she may gracefully hover horizontally (left or right) as long as she doesn't overlap with any snake (including exactly at one of its endpoints). +She may also move vertically (up or down) as long as she's overlapping with a ladder (including exactly at one of its endpoints). +Flynn always moves continuously around the plane (she does not skip from one integral coordinate to the next). +

+ +

+Sneider the Snake doesn't want Flynn to reach her destination, just because he likes being mean. +Determine the minimum possible sum of lengths of snakes which Sneider must place such that Flynn will be unable to reach coordinates (0, H) from her initial position (0, 0), if possible. +

+ + +

Input

+ +

+Input begins with an integer T, the number of rooms. +For each room, there is first a line containing the space-separated integers N and H. +Then, N lines follow, the ith of which contains the space-separated integers +Xi, Ai, and Bi. +

+ + +

Output

+ +

+For the ith room, print a line containing "Case #i: " +followed by 1 integer, either the minimum total length of snakes required, or -1 if Sneider cannot prevent Flynn from reaching coordinates (0, H). +

+ + +

Constraints

+ +

+1 ≤ T ≤ 150
+1 ≤ N ≤ 50
+1 ≤ H ≤ 100,000
+0 ≤ Xi ≤ 100,000
+0 ≤ Ai < BiH
+0 ≤ xj
+0 < ajbj < H
+

+ +

Explanation of Sample

+ +

+In the first case, one optimal way for Sneider to prevent Flynn from reaching coordinates (0, 4) involves placing a length-2 snake with endpoints (0.5, 1) and (0.5, 3), as illustrated below (with ladders indicated in brown and the snake indicated in green): +

+ + + +

+In the second case, Flynn already can't reach coordinates (0, 100) even if Sneider doesn't place any snakes. +

+ +

+In the third case, Flynn cannot be prevented from reaching coordinates (0, 9). +

+ +

+In the fourth case, one optimal way for Sneider to prevent Flynn from reaching coordinates (0, 30) involves placing a length-1 snake with endpoints (9, 20) and (9, 21), +two length-0 snakes at coordinates (14, 20) and (16, 20), and a length-2 snake with endpoints (24, 20) and (24, 22). The sum of these snakes' lengths is 1 + 0 + 0 + 2 = 3. +

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383 +9 288 536 +19 6 440 +18 231 +26 61 231 +20 0 217 +37 84 147 +28 31 224 +12 0 221 +17 0 212 +0 75 153 +22 63 231 +16 2 130 +27 118 231 +24 0 83 +18 0 216 +8 126 231 +5 2 138 +38 42 231 +7 0 221 +1 35 231 +31 52 231 diff --git a/2019/round1/ladders_and_snakes.md b/2019/round1/ladders_and_snakes.md new file mode 100644 index 0000000000000000000000000000000000000000..a0bbb00acbff03e43539c7a2ca0696d31424f049 --- /dev/null +++ b/2019/round1/ladders_and_snakes.md @@ -0,0 +1,67 @@ +**N** ladders have been set up in a room, which can be represented as a 2D plane when viewed from the side. The room's floor is the horizontal line with y-coordinate 0, and its ceiling is the horizontal line with y-coordinate **H**. The _i_th ladder is a vertical line segment between integral coordinates (**Xi**, **Ai**) and (**Xi**, **Bi**), located within the inclusive bounds of the room (such that 0 ≤ **Ai** < **Bi** ≤ **H**). Note that each ladder may be touching the floor and/or ceiling, or may be floating in mid-air (don't question it). No two ladders overlap with one another (even at their endpoints). + +Sneider the Snake has taken an interest in this room, and may add 0 or more +snakes to it. The _j_th snake will be a vertical line segment between some +coordinates (**xj**, **aj**) and (**xj**, **bj**), located strictly inside the +bounds of the room (with **xj** being any non-negative real number, and **aj** +and **bj** being integers such that 0 < **aj** ≤ **bj** < **H**). A snake may +be a length-0 line segment, with its endpoints being equal, in which case it +occupies only a single point on the plane. No snake may overlap with any other +snake, nor with any ladder (even at an endpoint). + +Flynn the Flying Squirrel finds herself on the floor at coordinates (0, 0), +and wants to reach coordinates (0, **H**) on the ceiling. At any point, she +may gracefully hover horizontally (left or right) as long as she doesn't +overlap with any snake (including exactly at one of its endpoints). She may +also move vertically (up or down) as long as she's overlapping with a ladder +(including exactly at one of its endpoints). Flynn always moves continuously +around the plane (she does not skip from one integral coordinate to the next). + +Sneider the Snake doesn't want Flynn to reach her destination, just because he +likes being mean. Determine the minimum possible sum of lengths of snakes +which Sneider must place such that Flynn will be unable to reach coordinates +(0, **H**) from her initial position (0, 0), if possible. + +### Input + +Input begins with an integer **T**, the number of rooms. For each room, there +is first a line containing the space-separated integers **N** and **H**. Then, +**N** lines follow, the _i_th of which contains the space-separated integers +**Xi**, **Ai**, and **Bi**. + +### Output + +For the _i_th room, print a line containing "Case #_i_: " followed by 1 +integer, either the minimum total length of snakes required, or -1 if Sneider +cannot prevent Flynn from reaching coordinates (0, **H**). + +### Constraints + +1 ≤ **T** ≤ 150 +1 ≤ **N** ≤ 50 +1 ≤ **H** ≤ 100,000 +0 ≤ **Xi** ≤ 100,000 +0 ≤ **Ai** < **Bi** ≤ **H** +0 ≤ **xj** +0 < **aj** ≤ **bj** < **H** + +### Explanation of Sample + +In the first case, one optimal way for Sneider to prevent Flynn from reaching +coordinates (0, 4) involves placing a length-2 snake with endpoints (0.5, 1) +and (0.5, 3), as illustrated below (with ladders indicated in brown and the +snake indicated in green): + +![]({{PHOTO_ID:262526658147947}}) + +In the second case, Flynn already can't reach coordinates (0, 100) even if +Sneider doesn't place any snakes. + +In the third case, Flynn cannot be prevented from reaching coordinates (0, 9). + +In the fourth case, one optimal way for Sneider to prevent Flynn from reaching +coordinates (0, 30) involves placing a length-1 snake with endpoints (9, 20) +and (9, 21), two length-0 snakes at coordinates (14, 20) and (16, 20), and a +length-2 snake with endpoints (24, 20) and (24, 22). The sum of these snakes' +lengths is 1 + 0 + 0 + 2 = 3. + diff --git a/2019/round1/ladders_and_snakes.out b/2019/round1/ladders_and_snakes.out new file mode 100644 index 0000000000000000000000000000000000000000..bd36a4223d222b459d2f31668978b26feea53ae1 --- /dev/null +++ b/2019/round1/ladders_and_snakes.out @@ -0,0 +1,410 @@ +Case #1: -1 +Case #2: 128 +Case #3: 1304 +Case #4: 4899902 +Case #5: 486 +Case #6: -1 +Case #7: 765 +Case #8: 2 +Case #9: 4465 +Case #10: 4176 +Case #11: 978 +Case #12: 7982 +Case #13: -1 +Case #14: 1185 +Case #15: 295 +Case #16: 2972 +Case #17: -1 +Case #18: 0 +Case #19: 752 +Case #20: 1558 +Case #21: 1037 +Case #22: 6626 +Case #23: 2500 +Case #24: 707 +Case #25: 1057 +Case #26: 1817 +Case #27: 5104 +Case #28: 8208 +Case #29: 2146 +Case #30: -1 +Case #31: 1255 +Case #32: -1 +Case #33: 70 +Case #34: -1 +Case #35: 2231 +Case #36: 664 +Case #37: -1 +Case #38: 855 +Case #39: -1 +Case #40: 364 +Case #41: -1 +Case #42: -1 +Case #43: 2618 +Case #44: 526 +Case #45: -1 +Case #46: 2801 +Case #47: 6289 +Case #48: 647 +Case #49: 3844 +Case #50: 280 +Case #51: -1 +Case #52: 407 +Case #53: 960 +Case #54: 12909 +Case #55: 2337 +Case #56: 2039 +Case #57: 2268 +Case #58: 12594 +Case #59: 3276 +Case #60: 2429 +Case #61: 5127 +Case #62: 7 +Case #63: 3574 +Case #64: 8288 +Case #65: 9457 +Case #66: 1437 +Case #67: 2594 +Case #68: 7941 +Case #69: 1463496 +Case #70: 466 +Case #71: 1878 +Case #72: 2733 +Case #73: 2978 +Case #74: 1692 +Case #75: 1425 +Case #76: 3058 +Case #77: 276 +Case #78: -1 +Case #79: -1 +Case #80: 8566 +Case #81: -1 +Case #82: 8397 +Case #83: -1 +Case #84: 608 +Case #85: 1205 +Case #86: 6786 +Case #87: 74 +Case #88: -1 +Case #89: -1 +Case #90: 1329 +Case #91: 1784 +Case #92: 3360 +Case #93: 2009 +Case #94: -1 +Case #95: 1692 +Case #96: 6334 +Case #97: -1 +Case #98: 2252 +Case #99: 3785 +Case #100: 1691 +Case #101: -1 +Case #102: 1135 +Case #103: 2137 +Case #104: 383 +Case #105: 689 +Case #106: -1 +Case #107: 8585 +Case #108: 1773 +Case #109: 3981 +Case #110: 905 +Case #111: -1 +Case #112: 0 +Case #113: 873 +Case #114: -1 +Case #115: 3494 +Case #116: 3099 +Case #117: 3486 +Case #118: 0 +Case #119: 49 +Case #120: -1 +Case #121: 4309 +Case #122: -1 +Case #123: 242 +Case #124: 3163 +Case #125: 7327 +Case #126: 10890 +Case #127: 9100 +Case #128: -1 +Case #129: 4218 +Case #130: 49 +Case #131: -1 +Case #132: -1 +Case #133: 2207 +Case #134: 724 +Case #135: 0 +Case #136: 0 +Case #137: 3681 +Case #138: 1564 +Case #139: 7680 +Case #140: 0 +Case #141: -1 +Case #142: 13345 +Case #143: 3997 +Case #144: -1 +Case #145: 0 +Case #146: -1 +Case #147: 0 +Case #148: 1631302 +Case #149: 16022 +Case #150: 574 +Case #151: 207 +Case #152: -1 +Case #153: 237 +Case #154: 963 +Case #155: -1 +Case #156: 0 +Case #157: 1884 +Case #158: 467 +Case #159: 2154 +Case #160: 0 +Case #161: 153 +Case #162: 1984 +Case #163: -1 +Case #164: 2818 +Case #165: 736 +Case #166: 8663 +Case #167: 801 +Case #168: 531 +Case #169: 0 +Case #170: 3577 +Case #171: -1 +Case #172: -1 +Case #173: -1 +Case #174: 1082 +Case #175: 5504 +Case #176: 0 +Case #177: -1 +Case #178: 3162 +Case #179: 1352 +Case #180: -1 +Case #181: 1192 +Case #182: -1 +Case #183: 9102 +Case #184: 695 +Case #185: 3826 +Case #186: 2175 +Case #187: -1 +Case #188: 4079 +Case #189: 3782 +Case #190: 314 +Case #191: 793 +Case #192: 6519 +Case #193: 2131 +Case #194: -1 +Case #195: 7086 +Case #196: 4906 +Case #197: 6865 +Case #198: 0 +Case #199: 5310 +Case #200: 9515 +Case #201: 0 +Case #202: 1496 +Case #203: -1 +Case #204: 6 +Case #205: 0 +Case #206: 6945 +Case #207: 135 +Case #208: 1896 +Case #209: -1 +Case #210: 2242 +Case #211: 678 +Case #212: 1258 +Case #213: 4120 +Case #214: 9291 +Case #215: 3427 +Case #216: 2854 +Case #217: 2951 +Case #218: 129 +Case #219: 5476 +Case #220: -1 +Case #221: 3835 +Case #222: 7646 +Case #223: 5658 +Case #224: 1772 +Case #225: 2981 +Case #226: -1 +Case #227: 8914 +Case #228: 3025 +Case #229: 332 +Case #230: 0 +Case #231: -1 +Case #232: 103 +Case #233: 12 +Case #234: 7327 +Case #235: 3024 +Case #236: 7723 +Case #237: 3808 +Case #238: -1 +Case #239: -1 +Case #240: 426 +Case #241: -1 +Case #242: -1 +Case #243: 50 +Case #244: 5136 +Case #245: -1 +Case #246: 5686 +Case #247: 8075 +Case #248: -1 +Case #249: 4237 +Case #250: 2218 +Case #251: 4057 +Case #252: 4771 +Case #253: 6254 +Case #254: 0 +Case #255: 1835 +Case #256: 364 +Case #257: 8081 +Case #258: 7835 +Case #259: 3626 +Case #260: 1948 +Case #261: 1591 +Case #262: 334 +Case #263: 3523 +Case #264: 0 +Case #265: 1658 +Case #266: -1 +Case #267: 3871 +Case #268: 4204 +Case #269: -1 +Case #270: 1379 +Case #271: -1 +Case #272: 1069 +Case #273: -1 +Case #274: 682 +Case #275: -1 +Case #276: 162 +Case #277: 76 +Case #278: 3565 +Case #279: -1 +Case #280: 7030 +Case #281: 667 +Case #282: 6777 +Case #283: -1 +Case #284: -1 +Case #285: 4625 +Case #286: 9137 +Case #287: 2501 +Case #288: 0 +Case #289: 3443 +Case #290: 5183 +Case #291: 482 +Case #292: 1214541 +Case #293: 944 +Case #294: 0 +Case #295: -1 +Case #296: 4121 +Case #297: 2392 +Case #298: 3881 +Case #299: 3318 +Case #300: 3439 +Case #301: 4895 +Case #302: 640 +Case #303: -1 +Case #304: -1 +Case #305: 5091 +Case #306: 4373 +Case #307: 2330 +Case #308: 0 +Case #309: 5 +Case #310: 5521 +Case #311: 1290033 +Case #312: 5354 +Case #313: 5952 +Case #314: 3846 +Case #315: 870 +Case #316: 9408 +Case #317: 2176 +Case #318: 6935 +Case #319: 0 +Case #320: 1340 +Case #321: 213 +Case #322: 220 +Case #323: 4360 +Case #324: 2567 +Case #325: 104 +Case #326: -1 +Case #327: 11660 +Case #328: 7598 +Case #329: -1 +Case #330: 6574 +Case #331: -1 +Case #332: -1 +Case #333: 9329 +Case #334: 7602 +Case #335: 3871 +Case #336: -1 +Case #337: -1 +Case #338: 4893 +Case #339: -1 +Case #340: 1715 +Case #341: -1 +Case #342: 1491 +Case #343: 538 +Case #344: -1 +Case #345: 165 +Case #346: 282 +Case #347: 5461 +Case #348: 3233 +Case #349: 2254 +Case #350: 45 +Case #351: 0 +Case #352: 0 +Case #353: 0 +Case #354: 3147 +Case #355: -1 +Case #356: 731 +Case #357: 1047 +Case #358: 7301 +Case #359: 3 +Case #360: 5599 +Case #361: 679 +Case #362: 876 +Case #363: 1865 +Case #364: 9510 +Case #365: -1 +Case #366: 1077830 +Case #367: 476 +Case #368: 0 +Case #369: 0 +Case #370: 1124 +Case #371: 1689 +Case #372: 7486 +Case #373: -1 +Case #374: 1809 +Case #375: 2941 +Case #376: -1 +Case #377: 0 +Case #378: 7982 +Case #379: 7585 +Case #380: 1468447 +Case #381: 1439 +Case #382: 502 +Case #383: 1077900 +Case #384: 2844 +Case #385: -1 +Case #386: 391 +Case #387: 5845 +Case #388: -1 +Case #389: 2211 +Case #390: 10151 +Case #391: 1385 +Case #392: 257 +Case #393: 3728 +Case #394: 942 +Case #395: 1723 +Case #396: 2818 +Case #397: 1384 +Case #398: 1134 +Case #399: 0 +Case #400: -1 +Case #401: -1 +Case #402: 2813 +Case #403: 0 +Case #404: -1 +Case #405: 1276 +Case #406: 237 +Case #407: 2330 +Case #408: 646 +Case #409: 3159 +Case #410: 606 diff --git a/2019/round2/bitstrings_as_a_service.cpp b/2019/round2/bitstrings_as_a_service.cpp new file mode 100644 index 0000000000000000000000000000000000000000..b20ebb9135a47afc2b03c8ad7dd0e6bc745a87fa --- /dev/null +++ b/2019/round2/bitstrings_as_a_service.cpp @@ -0,0 +1,169 @@ +// Bitstrings as a Service +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +#define LIM 4001 + +int N,M,K; +int comp[LIM],sz[LIM],val[LIM]; +vector con[LIM]; +int dyn[LIM][LIM]; + +void rec(int i) +{ + if (comp[i]>=0) + return; + comp[i]=K; + sz[K]++; + int j; + Fox(j,Sz(con[i])) + rec(con[i][j]); +} + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int i,j; + // testcase loop + Read(T); + Fox1(t,T) + { + // init + Fox(i,N) + con[i].clear(); + // input, and create graph of bit equalities + Read(N),Read(M); + while (M--) + { + Read(i),Read(j),i--,j--; + while (j>i) + { + con[i].pb(j); + con[j].pb(i); + i++,j--; + } + } + // find all components of equal bits + K=0; + Fill(sz,0); + Fill(comp,-1); + Fox(i,N) + if (comp[i]<0) + { + rec(i); + K++; + } + // DP on component value assignments + Fill(dyn,-1); + dyn[0][0]=0; + Fox(i,K) + Fox(j,N) + if (dyn[i][j]>=0) + dyn[i+1][j]=dyn[i+1][j+sz[i]]=j; + // trace back to assign values to components + Fox(i,N+1) + { + if (dyn[K][j=N/2+i]>=0) + break; + if (dyn[K][j=N/2-i]>=0) + break; + } + FoxR1(i,K) + { + val[i-1]=(dyn[i][j]==j ? 0 : 1); + j=dyn[i][j]; + } + // output + printf("Case #%d: ",t); + Fox(i,N) + printf("%d",val[comp[i]]); + printf("\n"); + } + return(0); +} \ No newline at end of file diff --git a/2019/round2/bitstrings_as_a_service.html b/2019/round2/bitstrings_as_a_service.html new file mode 100644 index 0000000000000000000000000000000000000000..cc754f9e448c8a5b58e592f862a388e1934697a1 --- /dev/null +++ b/2019/round2/bitstrings_as_a_service.html @@ -0,0 +1,87 @@ +

+Carlos knows that the key to sustained customer loyalty is early customer acquisition and constant re-engagement. +With that in mind, he's setting his sights on sugary cereals. Kids love it, and they keep coming back for more. +He has a proposal for Post, the well-known manufacturer of Alpha-Bits: +

+ +

+ +"For 60 years these bits have been made of letters, but kids today are tired of letters for breakfast. Let me show you something truly revolutionary: bits made of numbers!" + +

+ +

+The executives at Post would like to assess the feasibility of producing numeric bits. In particular, they want to see if Carlos +can create a string of bits, B, of length N. In this string, each character is either '0' or '1'. +

+ +

+Carlos has been given a list of M requirements. The ith requirement states that the substring BXi...Yi +must be a palindrome. The new cereal surely won't succeed without appealing to children's acute sense of symmetry. +

+ +

+Furthermore, the number of zeroes and ones in B must be as close as possible. +In other words, if C(b) is the number of occurrences of bit b in B, +then the absolute difference |C(0) - C(1)| must be minimized. The margins on cereal are razor thin, and as everybody knows, bits are produced in pairs, so it's wasteful to use more of one sort than the other. +

+ +

+Help Carlos build any bitstring B consistent with all of these requirements (and with minimal difference between the number of zeroes and ones). +It's guaranteed that such a bitstring exists for every given set of requirements. +

+ + +

Input

+ +

+Input begins with an integer T, the number of bitstrings that Post has commissioned. +For each bitstring, there is first a line containing the space-separated integers N and M. +Then, M lines follow, the ith of which contains the space-separated integers +Xi and Yi. +

+ + +

Output

+ +

+For the ith commission, print a line containing "Case #i: " followed by a valid bitstring B. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 350
+1 ≤ N ≤ 4,000
+0 ≤ M ≤ 10,000
+1 ≤ XiYiN
+

+ + +

Explanation of Sample

+ +

+In the first case, the minimum absolute difference between the number of zeroes and ones is 0 (with 2 of each). +5 other outputs would also be accepted for this case: "0011", "0101", "0110", "1001", and "1010". For each of the remaining sample cases, various other outputs would similarly be accepted. +

+ +

+In the second case, the minimum achievable difference is 2. +

+ +

+In the third case, the minimum achievable difference is 2. +

+ +

+In the fourth case, the minimum achievable difference is 1. +

+ +

+In the fifth case, the minimum achievable difference is 0. +

+ +

+In the sixth case, the minimum achievable difference is 9. +

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70 +24 28 +2 3 +46 60 +44 61 +3 18 +37 52 +37 40 +20 36 +26 36 +32 12 +21 31 +4 12 +1 19 +19 31 +3 8 +15 32 +2 19 +5 19 +2 19 +9 14 +9 11 +6 23 +10 2 +5 5 +4 10 +44 18 +13 13 +10 13 +16 18 +3 8 +16 29 +33 40 +25 32 +19 26 +40 42 +7 14 +22 29 +24 34 +32 42 +11 15 +30 42 +28 40 +24 41 +3 9 +91 17 +11 23 +18 33 +73 83 +36 47 +43 56 +40 52 +51 68 +16 19 +14 21 +60 77 +45 59 +52 64 +20 34 +32 42 +41 44 +66 76 +32 44 +51 2 +43 47 +17 25 +28 1 +8 17 diff --git a/2019/round2/bitstrings_as_a_service.md b/2019/round2/bitstrings_as_a_service.md new file mode 100644 index 0000000000000000000000000000000000000000..da92fd2e2d7c2701057428bb56098769995039e2 --- /dev/null +++ b/2019/round2/bitstrings_as_a_service.md @@ -0,0 +1,66 @@ +Carlos knows that the key to sustained customer loyalty is early customer +acquisition and constant re-engagement. With that in mind, he's setting his +sights on sugary cereals. Kids love it, and they keep coming back for more. He +has a proposal for Post, the well-known manufacturer of Alpha-Bits: + +_ "For 60 years these bits have been made of letters, but kids today are tired +of letters for breakfast. Let me show you something truly revolutionary: bits +made of numbers!" _ + +The executives at Post would like to assess the feasibility of producing +numeric bits. In particular, they want to see if Carlos can create a string of +bits, **B**, of length **N**. In this string, each character is either `'0'` +or `'1'`. + +Carlos has been given a list of **M** requirements. The _i_th requirement +states that the substring **BXi...Yi** must be a palindrome. The new cereal +surely won't succeed without appealing to children's acute sense of symmetry. + +Furthermore, the number of zeroes and ones in **B** must be as close as +possible. In other words, if `C(b)` is the number of occurrences of bit _b_ in +**B**, then the absolute difference `|C(0) - C(1)|` must be minimized. The +margins on cereal are razor thin, and as everybody knows, bits are produced in +pairs, so it's wasteful to use more of one sort than the other. + +Help Carlos build any bitstring **B** consistent with all of these +requirements (and with minimal difference between the number of zeroes and +ones). It's guaranteed that such a bitstring exists for every given set of +requirements. + +### Input + +Input begins with an integer **T**, the number of bitstrings that Post has +commissioned. For each bitstring, there is first a line containing the space- +separated integers **N** and **M**. Then, **M** lines follow, the _i_th of +which contains the space-separated integers **Xi** and **Yi**. + +### Output + +For the _i_th commission, print a line containing "Case #_i_: " followed by a +valid bitstring **B**. + +### Constraints + +1 ≤ **T** ≤ 350 +1 ≤ **N** ≤ 4,000 +0 ≤ **M** ≤ 10,000 +1 ≤ **Xi** ≤ **Yi** ≤ **N** + +### Explanation of Sample + +In the first case, the minimum absolute difference between the number of +zeroes and ones is 0 (with 2 of each). **5 other outputs would also be +accepted** for this case: "0011", "0101", "0110", "1001", and "1010". **For +each of the remaining sample cases, various other outputs would similarly be +accepted.** + +In the second case, the minimum achievable difference is 2. + +In the third case, the minimum achievable difference is 2. + +In the fourth case, the minimum achievable difference is 1. + +In the fifth case, the minimum achievable difference is 0. + +In the sixth case, the minimum achievable difference is 9. + diff --git a/2019/round2/bitstrings_as_a_service.out b/2019/round2/bitstrings_as_a_service.out new file mode 100644 index 0000000000000000000000000000000000000000..e192f078b88f077401d76bc7fff883a76e8924ad --- /dev/null +++ b/2019/round2/bitstrings_as_a_service.out @@ -0,0 +1,509 @@ +Case #1: 1100 +Case #2: 110011 +Case #3: 1101 +Case #4: 01010 +Case #5: 1001100011 +Case #6: 0001100011001000000000111 +Case #7: 01010 +Case #8: 00000 +Case #9: 00011 +Case #10: 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111111111111111111111111100000000000000000000000000 +Case #509: 1111110111100111100000000000 diff --git a/2019/round2/grading.cpp b/2019/round2/grading.cpp new file mode 100644 index 0000000000000000000000000000000000000000..62de56a1c3be001b0fea942e8d2596421e9aba59 --- /dev/null +++ b/2019/round2/grading.cpp @@ -0,0 +1,156 @@ +// Grading +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +#define LIM 302 +#define LIM2 90001 + +int H,S,K; +char P[LIM][LIM]; + +// dyn[i][s][p] = min discards for at most s context switches in the first i papers in stack, +// with current paper type being p +int dyn[LIM][LIM][2]; + +// minD[f][s] = min total discards for at most s context switches assuming first paper type is f +int minD[2][LIM]; + +// ans[d] = min total context switches for at most d discards +int ans[LIM2]; + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int i,j,f,s,p,d; + // testcase loop + Read(T); + Fox1(t,T) + { + // input + Read(H),Read(S),Read(K); + Fox(i,H) + scanf("%s",&P[i]); + // DP on each stack + Fill(minD,0); + Fox(f,2) + Fox(j,S) + { + Fill(dyn,60); + Fox(s,H+1) + dyn[0][s][f]=0; + Fox(i,H) + Fox(s,H+1) + Fox(p,2) + { + d=dyn[i][s][p]; + int p2=P[i][j]-'A'; + Min(dyn[i+1][s+(p2==p ? 0 : 1)][p2],d); // grade + Min(dyn[i+1][s][p],d+1); // discard + } + Fox(s,H+1) + minD[f][s]+=min(dyn[H][s][0],dyn[H][s][1]); + } + // compute answers + Fill(ans,60); + Fox(f,2) + Fox(s,H+1) + Min(ans[minD[f][s]],s); + Fox(d,H*S) + Min(ans[d+1],ans[d]); + // process queries + printf("Case #%d:",t); + while (K--) + { + Read(d); + printf(" %d",ans[d]+1); + } + printf("\n"); + } + return(0); +} \ No newline at end of file diff --git a/2019/round2/grading.html b/2019/round2/grading.html new file mode 100644 index 0000000000000000000000000000000000000000..47c8a60e0fe0d566ec47651cf5ac2c54aca7ce1e --- /dev/null +++ b/2019/round2/grading.html @@ -0,0 +1,82 @@ +

+Due to a convenient recent teaching vacancy, Laz Y. has suddenly landed a job as a schoolteacher. +Known to his students as Mr. Y, he's prepared to provide a comprehensive, fairly-evaluated educational experience — as long as it doesn't take too much effort. +

+ +

+Mr. Y's first order of business in his new role will be grading recent exams from two different subjects: art and biology. +He has been handed S stacks of H exam papers each. The ith paper from the top in the jth stack is either from the art exam +(if Pi,j = "A"), or otherwise from the biology exam (if Pi,j = "B"). +

+ +

+Mr. Y will go about the grading process as follows: At each point in time, he'll select a stack which still contains at least one exam paper, and remove its topmost paper. +He'll then either grade that paper, or accidentally "lose" it and assign its owner a random grade instead. Either way, once he's done with that paper, +he'll repeat the process of selecting a new paper until all of the stacks are empty and all H*S papers have been dealt with. +

+ +

+There are few things that Mr. Y hates as much as context switching. For example, it's very troublesome to jump from grading an art exam to a biology one! +(Or from relaxing to doing any work at all.) Each time Mr. Y begins a grading a paper, he must make a context switch if this is either the first paper he's choosing to grade, or if its subject is different than that of the previous paper that he graded. Note that this entirely excludes any "lost" papers. +

+ +

+Mr. Y is no fool — he realizes that his evaluations would be too suspiciously inaccurate if he were to simply lose all H*S papers. +Even losing a smaller number of them may prove too suspicious. Therefore, he'll imagine K different theoretical scenarios, such that in the ith one, +he will allow himself to lose at most Li papers throughout the grading process (with L1..K all being distinct). +Independently for each scenario, he'd like to determine the minimum number of context switches he would need to make throughout the process. +

+ + +

Input

+ +

+Input begins with an integer T, the number of days Mr. Y spends grading exams. +For each day, there is first a line containing the space-separated integers H, S, and K. +Then, H lines follow, the ith of which contains the length-S string Pi,1..S. +Then, a final line follows containing the K space-separated integers L1 through LK. +

+ + +

Output

+ +

+For the ith day, print a line containing "Case #i: " followed by K space-separated integers, +the jth of which is the minimum number of context switches which Mr. Y would need to make if he were to grade the papers while losing at most +Lj of them. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 200
+1 ≤ H, S ≤ 300
+1 ≤ KH * S
+0 ≤ LiH * S - 1
+

+ + +

Explanation of Sample

+ +

+In the first case, if Mr. Y may only lose one paper, the best he can do is make two context switches, for example by grading the B papers from the first and third stacks, +then losing the B paper from the fifth stack, and then grading the A papers from the second and fourth stacks. +On the other hand, the freedom to lose two papers would allow him to make only one context switch, +for example by losing the A papers from the second and fourth stacks and then grading the B papers from the first, third, and fifth stacks. +

+ +

+In the second case, if Mr. Y may lose one paper, one optimal strategy (requiring just two context switches) is as follows: +

+ +
    +
  1. Grade the B paper from the top of stack 2 (first context switch). +
  2. Lose the A paper from the top of stack 3. +
  3. Grade the B paper from the top of stack 3. +
  4. Grade the A paper from the top of stack 1 (second context switch). +
  5. Grade the A paper from the top of stack 1. +
  6. Grade the A paper from the top of stack 2. +
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129 75 131 261 19 +10 7 70 +BBBBBBB +AAAABBB +BAAAAAB +AABAABB +BBAABBA +ABABABB +AAAABAB +AAABABA +BBBABAB +BBAAAAA +7 19 9 10 59 45 51 34 21 18 22 25 53 56 68 28 42 58 35 4 8 33 31 43 2 41 36 54 62 63 44 6 50 48 46 64 61 39 13 16 12 29 57 60 37 38 3 69 67 14 24 32 26 11 27 20 0 47 55 23 1 52 15 30 40 49 5 17 66 65 diff --git a/2019/round2/grading.md b/2019/round2/grading.md new file mode 100644 index 0000000000000000000000000000000000000000..c5598990dabb6f15b2e27355f94feec40daa1180 --- /dev/null +++ b/2019/round2/grading.md @@ -0,0 +1,77 @@ +Due to a convenient recent teaching vacancy, Laz Y. has suddenly landed a job +as a schoolteacher. Known to his students as Mr. Y, he's prepared to provide a +comprehensive, fairly-evaluated educational experience — as long as it doesn't +take too much effort. + +Mr. Y's first order of business in his new role will be grading recent exams +from two different subjects: art and biology. He has been handed **S** stacks +of **H** exam papers each. The _i_th paper from the top in the _j_th stack is +either from the art exam (if **Pi,j** = "A"), or otherwise from the biology +exam (if **Pi,j** = "B"). + +Mr. Y will go about the grading process as follows: At each point in time, +he'll select a stack which still contains at least one exam paper, and remove +its topmost paper. He'll then either grade that paper, or accidentally "lose" +it and assign its owner a random grade instead. Either way, once he's done +with that paper, he'll repeat the process of selecting a new paper until all +of the stacks are empty and all **H*****S** papers have been dealt with. + +There are few things that Mr. Y hates as much as context switching. For +example, it's very troublesome to jump from grading an art exam to a biology +one! (Or from relaxing to doing any work at all.) Each time Mr. Y begins a +grading a paper, he must make a context switch if this is either the first +paper he's choosing to grade, or if its subject is different than that of the +previous paper that he graded. Note that this entirely excludes any "lost" +papers. + +Mr. Y is no fool — he realizes that his evaluations would be too suspiciously +inaccurate if he were to simply lose all **H*****S** papers. Even losing a +smaller number of them may prove too suspicious. Therefore, he'll imagine +**K** different theoretical scenarios, such that in the _i_th one, he will +allow himself to lose at most **Li** papers throughout the grading process +(with **L1..K** all being distinct). Independently for each scenario, he'd +like to determine the minimum number of context switches he would need to make +throughout the process. + +### Input + +Input begins with an integer **T**, the number of days Mr. Y spends grading +exams. For each day, there is first a line containing the space-separated +integers **H**, **S**, and **K**. Then, **H** lines follow, the _i_th of which +contains the length-**S** string **Pi,1..S**. Then, a final line follows +containing the **K** space-separated integers **L1** through **LK**. + +### Output + +For the _i_th day, print a line containing "Case #_i_: " followed by **K** +space-separated integers, the _j_th of which is the minimum number of context +switches which Mr. Y would need to make if he were to grade the papers while +losing at most **Lj** of them. + +### Constraints + +1 ≤ **T** ≤ 200 +1 ≤ **H**, **S** ≤ 300 +1 ≤ **K** ≤ **H** * **S** +0 ≤ **Li** ≤ **H** * **S** \- 1 + +### Explanation of Sample + +In the first case, if Mr. Y may only lose one paper, the best he can do is +make two context switches, for example by grading the B papers from the first +and third stacks, then losing the B paper from the fifth stack, and then +grading the A papers from the second and fourth stacks. On the other hand, the +freedom to lose two papers would allow him to make only one context switch, +for example by losing the A papers from the second and fourth stacks and then +grading the B papers from the first, third, and fifth stacks. + +In the second case, if Mr. Y may lose one paper, one optimal strategy +(requiring just two context switches) is as follows: + + 1. Grade the B paper from the top of stack 2 (first context switch). + 2. Lose the A paper from the top of stack 3. + 3. Grade the B paper from the top of stack 3. + 4. Grade the A paper from the top of stack 1 (second context switch). + 5. Grade the A paper from the top of stack 1. + 6. Grade the A paper from the top of stack 2. + diff --git a/2019/round2/grading.out b/2019/round2/grading.out new file mode 100644 index 0000000000000000000000000000000000000000..83e09973e84fc9e594102ee8f7dc1948806bd0a8 --- /dev/null +++ b/2019/round2/grading.out @@ -0,0 +1,509 @@ +Case #1: 2 1 +Case #2: 2 3 1 +Case #3: 4 3 2 1 +Case #4: 3 5 2 1 2 4 +Case #5: 5 8 1 2 8 7 1 7 5 9 4 3 4 3 6 +Case #6: 1 +Case #7: 1 +Case #8: 1 1 +Case #9: 2 1 +Case #10: 301 241 1 1 1 225 298 90 1 272 242 1 292 1 62 115 1 144 1 1 46 124 292 55 1 160 1 294 1 130 6 179 1 1 220 236 1 1 1 160 1 1 1 264 300 1 262 194 1 138 210 1 1 31 1 261 1 1 164 236 1 46 234 1 1 1 72 286 1 166 192 1 202 1 117 1 140 1 86 284 1 1 1 178 1 148 1 240 10 274 68 36 170 130 1 55 194 1 1 86 262 220 18 1 1 1 193 1 1 128 1 1 192 124 282 1 204 1 1 204 208 228 1 1 1 1 174 1 212 1 1 1 56 1 213 1 88 52 1 192 1 1 1 1 1 1 1 1 104 264 210 1 18 60 150 1 1 236 1 1 271 1 114 233 1 1 1 238 1 1 190 27 1 1 1 1 60 1 52 158 36 1 1 1 30 6 1 1 184 298 1 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1 3 3 2 2 5 7 1 3 8 3 5 1 1 4 3 6 1 1 7 1 1 1 1 3 1 1 1 8 1 3 2 1 1 1 3 1 1 1 1 2 4 1 2 2 6 1 3 2 1 5 5 4 3 2 1 1 3 3 1 1 2 2 3 1 2 1 1 2 1 2 1 2 1 1 1 2 1 2 4 3 1 1 1 1 1 2 3 2 1 1 3 1 1 1 1 1 1 3 2 4 1 1 2 1 1 2 2 2 1 1 1 7 1 2 2 1 1 8 2 1 3 1 1 10 1 2 3 2 1 3 3 2 1 1 5 1 2 1 2 1 1 1 1 1 1 1 1 5 1 8 1 3 1 2 2 2 2 2 4 2 1 2 1 1 6 3 1 3 1 5 4 7 1 6 1 6 3 4 1 6 1 3 1 2 5 3 1 1 1 5 4 1 3 1 1 5 4 6 1 +Case #501: 1 2 2 1 1 2 1 1 2 1 1 1 1 1 1 2 1 1 1 4 1 1 4 1 2 1 1 1 1 1 3 6 2 2 1 2 1 1 1 1 1 1 1 1 2 4 1 1 3 1 1 1 1 +Case #502: 2 1 1 1 5 2 1 2 1 1 3 1 1 1 3 2 1 1 1 1 2 1 4 1 1 2 1 1 2 1 1 1 1 4 1 2 1 1 1 2 3 1 1 3 2 1 1 1 2 4 1 2 2 1 2 2 1 1 5 1 1 2 +Case #503: 3 1 1 5 2 11 4 1 13 1 2 1 1 3 3 1 4 1 12 4 2 14 1 1 1 1 2 1 1 17 2 1 2 1 3 1 1 1 12 1 1 4 1 1 8 2 1 1 2 6 3 19 2 1 2 1 1 1 8 1 8 1 8 1 1 6 1 6 +Case #504: 1 18 1 1 15 1 1 1 2 19 2 6 1 1 1 3 1 2 1 14 1 4 4 2 5 2 5 8 1 1 13 9 1 1 1 1 1 3 2 1 4 3 1 1 1 6 2 3 2 1 4 10 12 2 1 1 5 2 2 17 1 1 2 1 1 1 1 1 1 1 11 1 1 7 1 1 3 6 3 1 1 1 7 1 1 1 1 1 9 4 8 1 5 1 8 5 10 14 1 1 1 1 6 1 11 1 1 9 2 1 12 4 1 6 1 1 1 1 8 1 1 3 1 7 1 1 1 1 2 1 4 15 1 8 1 1 7 1 2 1 4 3 1 1 3 1 1 5 16 3 17 1 1 5 12 1 1 1 7 6 1 14 1 3 7 10 3 1 11 1 1 1 1 1 1 9 1 5 1 10 13 3 1 1 3 16 5 1 2 1 1 1 6 1 4 1 +Case #505: 1 4 7 1 2 1 1 1 5 6 1 7 2 1 13 3 1 1 3 1 6 8 2 4 3 1 2 1 4 1 1 1 1 1 7 1 12 7 1 1 9 6 5 1 1 1 1 5 1 1 1 5 1 1 5 15 1 1 4 2 1 2 10 3 1 1 1 4 1 2 2 1 2 1 +Case #506: 1 3 2 2 4 1 1 1 1 6 1 7 1 4 2 1 2 3 7 3 1 1 5 1 1 1 3 2 1 3 6 1 5 1 1 4 1 1 2 2 1 1 1 7 1 1 1 1 2 1 1 7 1 1 2 1 1 1 1 +Case #507: 2 1 1 1 1 1 3 8 1 6 5 4 2 1 1 4 +Case #508: 1 13 1 1 4 2 3 5 9 1 15 1 1 1 7 1 3 14 1 1 1 10 7 6 1 1 1 1 1 1 12 1 5 1 1 12 3 4 16 11 7 7 3 1 11 1 1 3 1 1 7 7 2 1 1 1 3 1 1 1 1 8 5 1 1 1 2 7 2 1 2 16 14 1 1 1 1 1 1 1 6 2 6 3 1 5 3 1 9 2 1 1 1 1 1 9 8 10 1 1 2 1 1 1 1 5 1 1 1 16 1 1 4 1 1 1 5 1 16 1 1 1 1 1 11 15 2 1 1 1 5 3 4 2 1 10 1 1 8 3 12 1 1 1 1 1 4 1 9 5 8 1 1 1 1 12 2 6 1 2 17 5 2 2 1 1 1 1 1 1 2 1 1 1 1 1 1 3 1 1 1 1 1 9 1 2 3 15 3 4 1 2 2 2 6 1 5 1 8 2 2 2 1 1 2 4 1 1 6 1 1 1 1 2 10 13 1 4 14 2 5 1 13 8 2 4 1 1 1 6 1 2 1 3 1 2 1 1 6 6 1 1 1 3 1 4 1 1 1 1 2 1 14 3 1 4 1 1 4 14 1 17 10 2 9 1 1 1 4 1 1 12 +Case #509: 5 2 5 4 1 1 1 1 2 3 2 2 1 1 1 2 1 1 1 6 5 2 2 1 6 1 1 1 1 1 1 6 1 1 1 1 1 1 4 3 4 2 1 1 1 1 6 1 1 4 2 2 2 4 2 2 8 1 1 2 7 1 3 2 1 1 6 3 1 1 diff --git a/2019/round2/on_the_run.cpp b/2019/round2/on_the_run.cpp new file mode 100644 index 0000000000000000000000000000000000000000..fcc136c95118bb9b406797d9f68f4a3633155cbb --- /dev/null +++ b/2019/round2/on_the_run.cpp @@ -0,0 +1,112 @@ +// On the Run +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int N,M,K; + int i,r,c; + int P[3]; + // testcase loop + Read(T); + Fox1(t,T) + { + // input + Read(N),Read(M),Read(K); + Fox(i,K+1) + { + Read(r),Read(c); + P[i]=(r+c)%2; + } + // output + printf("Case #%d: %c\n",t,(K==2 && P[1]==P[0] && P[2]==P[0]) ? 'Y' : 'N'); + } + return(0); +} \ No newline at end of file diff --git a/2019/round2/on_the_run.html b/2019/round2/on_the_run.html new file mode 100644 index 0000000000000000000000000000000000000000..46c1ee0f199c6887bf1f531fc71e1064cbf66440 --- /dev/null +++ b/2019/round2/on_the_run.html @@ -0,0 +1,78 @@ +

+The world's funniest schoolteacher has found himself in some trouble. Or, should we say, the world's funniest ex-schoolteacher. +On the basis of a false accusation regarding too many puns in his exam problems, Mr. X has not only been fired, but is now on the run from the Humane Association for Humour Administration (HAHA). +

+ +

+They've tracked Mr. X down to a yard in Scotland, which may be represented as a grid with N rows (numbered 1 to N) +and M columns (numbered 1 to M). Mr. X is initially in row A and column B. +There are also K (1 ≤ K ≤ 2) HAHA agents hot on his trail, +the ith of whom is initially in row Ri and column Ci. All K+1 individuals are in distinct cells. +

+ +

+The chase will then commence in an organized fashion as follows: +

+ +
    +
  1. +Each of the K HAHA agents in turn will move up, down, left, or right to an adjacent unoccupied cell* (without leaving the yard). +The agents may choose to move in any order, but each of them must move exactly once, and multiple of them may not move simultaneously. +It's guaranteed that all of the agents will always be able to move in some order for any possible state of the yard. +
  2. +
  3. +Mr. X will then attempt to similarly move to an adjacent unoccupied cell. If he's unable to move due to there being no unoccupied cells adjacent to him, he'll surrender quietly instead. +Otherwise, the process will repeat from Step 1. +
  4. +
+ +

+ * An unoccupied cell is one which currently contains neither Mr. X nor an agent. +

+ +

+Mr. X is hoping that, if he can avoid ever being forced to surrender, the HAHA agents may eventually leave him alone, +giving him the opportunity to slip away and work on regaining his teaching position. +However, the outcome of this chase seems difficult to call. Assuming that the agents work together optimally in an attempt to force Mr. X to surrender, while Mr. X optimally chooses moves to avoid surrendering indefinitely, determine whether or not he will eventually be forced to surrender. +

+ + +

Input

+ +

+Input begins with an integer T, the number of times that Mr. X is chased by HAHA agents. +For each chase, there is first a line containing the space-separated integers N, M, and K. +Then there is a line containing the space-separated integers A, and B. +Then, K lines follow, the ith of which contains the space-separated integers +Ri and Ci. +

+ + +

Output

+ +

+For the ith chase, print a line containing "Case #i: " +followed by one character, either "Y" if Mr. X will eventually be forced to surrender, or "N" otherwise. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 500
+3 ≤ N, M ≤ 300
+1 ≤ K ≤ 2
+1 ≤ A, RiN
+1 ≤ B, CiM
+

+ + +

Explanation of Sample

+ +

+In the first case, no matter how much time goes by and what moves the HAHA agent chooses to make, Mr. X can always avoid needing to surrender. +

+ +

+In the second case, if the first HAHA agent initially moves to cell (1, 2) and the second agent moves to cell (2, 1), then Mr. X will immediately be forced to surrender. +

diff --git a/2019/round2/on_the_run.in b/2019/round2/on_the_run.in new file mode 100644 index 0000000000000000000000000000000000000000..b1058afdf01a46f73dd41952e6fd099b8c54706e --- /dev/null +++ b/2019/round2/on_the_run.in @@ -0,0 +1,4043 @@ +1018 +3 3 1 +1 1 +2 2 +3 3 2 +1 1 +1 3 +3 1 +4 4 2 +1 2 +1 3 +1 4 +3 10 2 +2 10 +1 9 +3 9 +8 8 2 +8 1 +8 8 +1 1 +300 5 2 +2 3 +15 2 +300 5 +67 25 2 +32 10 +66 3 +21 18 +71 87 2 +36 44 +1 87 +71 1 +3 3 1 +1 1 +2 2 +3 3 2 +1 1 +1 3 +3 1 +7 7 2 +4 4 +1 7 +2 7 +3 10 2 +2 10 +1 9 +3 9 +8 8 2 +8 1 +8 8 +1 1 +300 5 2 +2 3 +15 2 +300 5 +67 25 2 +32 10 +66 3 +21 18 +71 87 2 +36 44 +1 87 +71 1 +300 300 2 +1 1 +1 2 +2 1 +300 300 2 +1 1 +1 3 +3 1 +3 3 2 +3 2 +1 2 +2 1 +3 3 2 +3 2 +2 3 +2 2 +3 3 2 +1 3 +2 2 +1 1 +3 3 2 +3 1 +3 3 +2 1 +3 3 2 +1 1 +2 2 +3 3 +3 3 2 +1 1 +3 3 +1 3 +3 3 2 +3 1 +3 2 +2 3 +3 3 2 +3 1 +1 3 +2 1 +3 3 2 +3 3 +3 2 +1 1 +3 3 2 +3 3 +3 2 +2 2 +3 3 2 +2 1 +1 3 +2 3 +3 3 2 +2 1 +1 3 +3 1 +3 3 2 +2 1 +1 3 +2 3 +3 3 2 +3 1 +2 3 +1 1 +3 3 2 +3 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+15 64 +264 181 +103 21 +268 149 2 +23 79 +91 30 +159 19 +256 16 2 +24 14 +88 12 +19 12 +249 262 2 +173 108 +144 110 +53 92 +22 55 2 +10 6 +1 5 +20 21 +294 106 2 +251 56 +19 44 +248 28 +6 34 2 +2 26 +1 19 +4 10 +158 63 2 +43 4 +33 57 +88 55 +219 195 2 +210 103 +85 22 +88 22 +70 6 2 +16 1 +47 6 +68 1 +43 180 2 +40 104 +14 48 +30 115 diff --git a/2019/round2/on_the_run.md b/2019/round2/on_the_run.md new file mode 100644 index 0000000000000000000000000000000000000000..38ef06c825e12a5cb91d383429bcffd4d0246b14 --- /dev/null +++ b/2019/round2/on_the_run.md @@ -0,0 +1,59 @@ +The world's funniest schoolteacher has found himself in some trouble. Or, +should we say, the world's funniest ex-schoolteacher. On the basis of a false +accusation regarding too many puns in his exam problems, Mr. X has not only +been fired, but is now on the run from the Humane Association for Humour +Administration (HAHA). + +They've tracked Mr. X down to a yard in Scotland, which may be represented as +a grid with **N** rows (numbered 1 to **N**) and **M** columns (numbered 1 to +**M**). Mr. X is initially in row **A** and column **B**. There are also **K** +(1 ≤ **K** ≤ 2) HAHA agents hot on his trail, the _i_th of whom is initially +in row **Ri** and column **Ci**. All **K**+1 individuals are in distinct +cells. + +The chase will then commence in an organized fashion as follows: + + 1. Each of the **K** HAHA agents in turn will move up, down, left, or right to an adjacent unoccupied cell* (without leaving the yard). The agents may choose to move in any order, but each of them must move exactly once, and multiple of them may not move simultaneously. It's guaranteed that all of the agents will always be able to move in some order for any possible state of the yard. + 2. Mr. X will then attempt to similarly move to an adjacent unoccupied cell. If he's unable to move due to there being no unoccupied cells adjacent to him, he'll surrender quietly instead. Otherwise, the process will repeat from Step 1. + +* _An unoccupied cell is one which currently contains neither Mr. X nor an agent._ + +Mr. X is hoping that, if he can avoid ever being forced to surrender, the HAHA +agents may eventually leave him alone, giving him the opportunity to slip away +and work on regaining his teaching position. However, the outcome of this +chase seems difficult to call. Assuming that the agents work together +optimally in an attempt to force Mr. X to surrender, while Mr. X optimally +chooses moves to avoid surrendering indefinitely, determine whether or not he +will eventually be forced to surrender. + +### Input + +Input begins with an integer **T**, the number of times that Mr. X is chased +by HAHA agents. For each chase, there is first a line containing the space- +separated integers **N**, **M**, and **K**. Then there is a line containing +the space-separated integers **A**, and **B**. Then, **K** lines follow, the +_i_th of which contains the space-separated integers **Ri** and **Ci**. + +### Output + +For the _i_th chase, print a line containing "Case #_i_: " followed by one +character, either "Y" if Mr. X will eventually be forced to surrender, or "N" +otherwise. + +### Constraints + +1 ≤ **T** ≤ 500 +3 ≤ **N**, **M** ≤ 300 +1 ≤ **K** ≤ 2 +1 ≤ **A**, **Ri** ≤ **N** +1 ≤ **B**, **Ci** ≤ **M** + +### Explanation of Sample + +In the first case, no matter how much time goes by and what moves the HAHA +agent chooses to make, Mr. X can always avoid needing to surrender. + +In the second case, if the first HAHA agent initially moves to cell (1, 2) and +the second agent moves to cell (2, 1), then Mr. X will immediately be forced +to surrender. + diff --git a/2019/round2/on_the_run.out b/2019/round2/on_the_run.out new file mode 100644 index 0000000000000000000000000000000000000000..06c280a7d70bd6ec3b4846e7c3d32858659b58c6 --- /dev/null +++ b/2019/round2/on_the_run.out @@ -0,0 +1,1018 @@ +Case #1: N +Case #2: Y +Case #3: N +Case #4: Y +Case #5: N +Case #6: Y +Case #7: N +Case #8: Y +Case #9: N +Case #10: Y +Case #11: N +Case #12: Y +Case #13: N +Case #14: Y +Case #15: N +Case #16: Y +Case #17: N +Case #18: Y +Case #19: Y +Case #20: N +Case #21: Y +Case #22: N +Case #23: Y +Case #24: Y +Case #25: N +Case #26: N +Case #27: N +Case #28: N +Case #29: N +Case #30: N +Case #31: N +Case #32: N +Case #33: N +Case #34: Y +Case #35: N +Case #36: N +Case #37: N +Case #38: N +Case #39: N +Case #40: N +Case #41: N +Case #42: N +Case #43: N +Case #44: N +Case #45: N +Case #46: N +Case #47: N +Case #48: N +Case #49: Y +Case #50: N +Case #51: N +Case #52: N +Case #53: N +Case #54: N +Case #55: N +Case #56: N +Case #57: N +Case #58: Y +Case #59: N +Case #60: N +Case #61: N +Case #62: N +Case #63: N +Case #64: N +Case #65: N +Case #66: N +Case #67: N +Case #68: N +Case #69: N +Case #70: N +Case #71: N +Case #72: N +Case #73: N +Case #74: N +Case #75: N +Case #76: N +Case #77: N +Case #78: N +Case #79: Y +Case #80: N +Case #81: N +Case #82: N +Case #83: N +Case #84: N +Case #85: N +Case #86: N +Case #87: N +Case #88: Y +Case #89: Y +Case #90: Y +Case #91: N +Case #92: N +Case #93: N +Case #94: N +Case #95: N +Case #96: N +Case #97: N +Case #98: N +Case #99: N +Case #100: Y +Case #101: Y +Case #102: N +Case #103: N +Case #104: N +Case #105: N +Case #106: N +Case #107: Y +Case #108: N +Case #109: N +Case #110: Y +Case #111: N +Case #112: N +Case #113: N +Case #114: N +Case #115: Y +Case #116: Y +Case #117: N +Case #118: N +Case #119: Y +Case #120: N +Case #121: N +Case #122: N +Case #123: N +Case #124: N +Case #125: N +Case #126: N +Case #127: N +Case #128: Y +Case #129: N +Case #130: N +Case #131: Y +Case #132: N +Case #133: N +Case #134: N +Case #135: N +Case #136: Y +Case #137: N +Case #138: N +Case #139: N +Case #140: N +Case #141: Y +Case #142: N +Case #143: N +Case #144: N +Case #145: N +Case #146: N +Case #147: Y +Case #148: N +Case #149: N +Case #150: N +Case #151: N +Case #152: N +Case #153: N +Case #154: N +Case #155: N +Case #156: N +Case #157: N +Case #158: Y +Case #159: N +Case #160: N +Case #161: N +Case #162: N +Case #163: N +Case #164: Y +Case #165: N +Case #166: Y +Case #167: N +Case #168: N +Case #169: N +Case #170: N +Case #171: N +Case #172: N +Case #173: Y +Case #174: N +Case #175: N +Case #176: N +Case #177: N +Case #178: N +Case #179: N +Case #180: N +Case #181: N +Case #182: N +Case #183: Y +Case #184: N +Case #185: Y +Case #186: N +Case #187: N +Case #188: Y +Case #189: N +Case #190: N +Case #191: N +Case #192: N +Case #193: N +Case #194: N +Case #195: Y +Case #196: N +Case #197: N +Case #198: Y +Case #199: N +Case #200: Y +Case #201: Y +Case #202: N +Case #203: N +Case #204: N +Case #205: Y +Case #206: N +Case #207: N +Case #208: N +Case #209: Y +Case #210: Y +Case #211: N +Case #212: N +Case #213: N +Case #214: N +Case #215: Y +Case #216: N +Case #217: N +Case #218: N +Case #219: N +Case #220: Y +Case #221: N +Case #222: N +Case #223: N +Case #224: Y +Case #225: Y +Case #226: N +Case #227: Y +Case #228: N +Case #229: N +Case #230: N +Case #231: N +Case #232: N +Case #233: Y +Case #234: Y +Case #235: N +Case #236: N +Case #237: N +Case #238: Y +Case #239: N +Case #240: N +Case #241: N +Case #242: N +Case #243: N +Case #244: N +Case #245: N +Case #246: N +Case #247: N +Case #248: N +Case #249: N +Case #250: Y +Case #251: N +Case #252: N +Case #253: N +Case #254: N +Case #255: N +Case #256: Y +Case #257: N +Case #258: N +Case #259: N +Case #260: N +Case #261: N +Case #262: Y +Case #263: N +Case #264: Y +Case #265: Y +Case #266: Y +Case #267: N +Case #268: N +Case #269: N +Case #270: N +Case #271: N +Case #272: N +Case #273: N +Case #274: N +Case #275: Y +Case #276: N +Case #277: N +Case #278: N +Case #279: Y +Case #280: Y +Case #281: Y +Case #282: N +Case #283: N +Case #284: Y +Case #285: N +Case #286: N +Case #287: N +Case #288: N +Case #289: N +Case #290: N +Case #291: N +Case #292: N +Case #293: Y +Case #294: N +Case #295: N +Case #296: N +Case #297: N +Case #298: Y +Case #299: N +Case #300: N +Case #301: Y +Case #302: N +Case #303: N +Case #304: N +Case #305: N +Case #306: N +Case #307: N +Case #308: N +Case #309: N +Case #310: Y +Case #311: Y +Case #312: N +Case #313: N +Case #314: Y +Case #315: N +Case #316: N +Case #317: Y +Case #318: Y +Case #319: N +Case #320: N +Case #321: N +Case #322: N +Case #323: N +Case #324: N +Case #325: N +Case #326: N +Case #327: N +Case #328: N +Case #329: Y +Case #330: N +Case #331: N +Case #332: N +Case #333: N +Case #334: Y +Case #335: N +Case #336: N +Case #337: Y +Case #338: N +Case #339: N +Case #340: N +Case #341: Y +Case #342: N +Case #343: N +Case #344: N +Case #345: N +Case #346: N +Case #347: N +Case #348: N +Case #349: N +Case #350: N +Case #351: N +Case #352: N +Case #353: Y +Case #354: N +Case #355: N +Case #356: N +Case #357: N +Case #358: N +Case #359: N +Case #360: N +Case #361: Y +Case #362: N +Case #363: N +Case #364: Y +Case #365: N +Case #366: N +Case #367: N +Case #368: Y +Case #369: N +Case #370: N +Case #371: N +Case #372: N +Case #373: N +Case #374: N +Case #375: N +Case #376: N +Case #377: N +Case #378: N +Case #379: N +Case #380: N +Case #381: N +Case #382: N +Case #383: Y +Case #384: N +Case #385: Y +Case #386: N +Case #387: N +Case #388: N +Case #389: N +Case #390: N +Case #391: N +Case #392: N +Case #393: Y +Case #394: N +Case #395: N +Case #396: N +Case #397: Y +Case #398: N +Case #399: N +Case #400: N +Case #401: N +Case #402: N +Case #403: N +Case #404: N +Case #405: N +Case #406: N +Case #407: Y +Case #408: Y +Case #409: N +Case #410: N +Case #411: Y +Case #412: N +Case #413: N +Case #414: Y +Case #415: N +Case #416: N +Case #417: N +Case #418: N +Case #419: Y +Case #420: N +Case #421: N +Case #422: N +Case #423: N +Case #424: Y +Case #425: N +Case #426: N +Case #427: N +Case #428: N +Case #429: N +Case #430: N +Case #431: N +Case #432: N +Case #433: Y +Case #434: Y +Case #435: Y +Case #436: N +Case #437: N +Case #438: N +Case #439: N +Case #440: N +Case #441: Y +Case #442: N +Case #443: Y +Case #444: N +Case #445: N +Case #446: N +Case #447: N +Case #448: N +Case #449: N +Case #450: N +Case #451: N +Case #452: N +Case #453: Y +Case #454: Y +Case #455: N +Case #456: Y +Case #457: N +Case #458: Y +Case #459: N +Case #460: Y +Case #461: N +Case #462: N +Case #463: N +Case #464: N +Case #465: N +Case #466: Y +Case #467: N +Case #468: N +Case #469: N +Case #470: N +Case #471: N +Case #472: N +Case #473: Y +Case #474: N +Case #475: Y +Case #476: N +Case #477: N +Case #478: N +Case #479: Y +Case #480: N +Case #481: N +Case #482: N +Case #483: N +Case #484: N +Case #485: Y +Case #486: N +Case #487: N +Case #488: N +Case #489: N +Case #490: N +Case #491: N +Case #492: N +Case #493: N +Case #494: N +Case #495: Y +Case #496: N +Case #497: Y +Case #498: N +Case #499: Y +Case #500: Y +Case #501: N +Case #502: N +Case #503: N +Case #504: N +Case #505: Y +Case #506: N +Case #507: N +Case #508: N +Case #509: N +Case #510: N +Case #511: N +Case #512: Y +Case #513: N +Case #514: N +Case #515: Y +Case #516: N +Case #517: N +Case #518: Y +Case #519: N +Case #520: N +Case #521: N +Case #522: N +Case #523: N +Case #524: N +Case #525: Y +Case #526: N +Case #527: Y +Case #528: N +Case #529: N +Case #530: N +Case #531: Y +Case #532: N +Case #533: Y +Case #534: N +Case #535: N +Case #536: N +Case #537: N +Case #538: N +Case #539: N +Case #540: Y +Case #541: N +Case #542: N +Case #543: N +Case #544: N +Case #545: N +Case #546: Y +Case #547: N +Case #548: N +Case #549: N +Case #550: N +Case #551: N +Case #552: N +Case #553: N +Case #554: N +Case #555: Y +Case #556: N +Case #557: N +Case #558: Y +Case #559: N +Case #560: N +Case #561: N +Case #562: Y +Case #563: N +Case #564: N +Case #565: N +Case #566: Y +Case #567: N +Case #568: N +Case #569: N +Case #570: N +Case #571: N +Case #572: N +Case #573: N +Case #574: N +Case #575: N +Case #576: N +Case #577: Y +Case #578: N +Case #579: N +Case #580: N +Case #581: N +Case #582: Y +Case #583: Y +Case #584: N +Case #585: N +Case #586: N +Case #587: N +Case #588: N +Case #589: N +Case #590: N +Case #591: N +Case #592: N +Case #593: N +Case #594: N +Case #595: Y +Case #596: N +Case #597: N +Case #598: N +Case #599: N +Case #600: N +Case #601: N +Case #602: N +Case #603: N +Case #604: N +Case #605: N +Case #606: N +Case #607: Y +Case #608: N +Case #609: Y +Case #610: N +Case #611: Y +Case #612: N +Case #613: N +Case #614: Y +Case #615: Y +Case #616: Y +Case #617: N +Case #618: N +Case #619: N +Case #620: N +Case #621: N +Case #622: N +Case #623: Y +Case #624: N +Case #625: N +Case #626: N +Case #627: Y +Case #628: N +Case #629: Y +Case #630: N +Case #631: Y +Case #632: N +Case #633: Y +Case #634: N +Case #635: N +Case #636: N +Case #637: N +Case #638: Y +Case #639: N +Case #640: N +Case #641: N +Case #642: N +Case #643: N +Case #644: Y +Case #645: Y +Case #646: N +Case #647: N +Case #648: N +Case #649: N +Case #650: Y +Case #651: N +Case #652: N +Case #653: N +Case #654: N +Case #655: N +Case #656: N +Case #657: N +Case #658: N +Case #659: N +Case #660: N +Case #661: N +Case #662: N +Case #663: N +Case #664: N +Case #665: N +Case #666: Y +Case #667: N +Case #668: N +Case #669: N +Case #670: Y +Case #671: N +Case #672: N +Case #673: Y +Case #674: N +Case #675: N +Case #676: N +Case #677: N +Case #678: N +Case #679: N +Case #680: N +Case #681: N +Case #682: Y +Case #683: N +Case #684: N +Case #685: N +Case #686: Y +Case #687: N +Case #688: N +Case #689: Y +Case #690: Y +Case #691: Y +Case #692: Y +Case #693: N +Case #694: N +Case #695: N +Case #696: N +Case #697: N +Case #698: Y +Case #699: N +Case #700: N +Case #701: N +Case #702: N +Case #703: Y +Case #704: N +Case #705: N +Case #706: N +Case #707: N +Case #708: N +Case #709: Y +Case #710: N +Case #711: N +Case #712: Y +Case #713: N +Case #714: N +Case #715: N +Case #716: Y +Case #717: Y +Case #718: N +Case #719: N +Case #720: N +Case #721: N +Case #722: N +Case #723: Y +Case #724: N +Case #725: Y +Case #726: N +Case #727: N +Case #728: N +Case #729: N +Case #730: N +Case #731: N +Case #732: N +Case #733: N +Case #734: N +Case #735: N +Case #736: N +Case #737: N +Case #738: N +Case #739: N +Case #740: Y +Case #741: Y +Case #742: N +Case #743: N +Case #744: N +Case #745: N +Case #746: N +Case #747: Y +Case #748: N +Case #749: Y +Case #750: Y +Case #751: Y +Case #752: N +Case #753: N +Case #754: N +Case #755: N +Case #756: N +Case #757: N +Case #758: N +Case #759: N +Case #760: N +Case #761: Y +Case #762: N +Case #763: N +Case #764: Y +Case #765: Y +Case #766: N +Case #767: N +Case #768: N +Case #769: Y +Case #770: N +Case #771: Y +Case #772: Y +Case #773: Y +Case #774: N +Case #775: Y +Case #776: Y +Case #777: N +Case #778: Y +Case #779: N +Case #780: N +Case #781: N +Case #782: N +Case #783: N +Case #784: N +Case #785: Y +Case #786: N +Case #787: Y +Case #788: Y +Case #789: N +Case #790: N +Case #791: N +Case #792: N +Case #793: N +Case #794: N +Case #795: N +Case #796: N +Case #797: N +Case #798: N +Case #799: N +Case #800: N +Case #801: N +Case #802: N +Case #803: N +Case #804: N +Case #805: N +Case #806: N +Case #807: N +Case #808: N +Case #809: N +Case #810: N +Case #811: N +Case #812: N +Case #813: N +Case #814: Y +Case #815: N +Case #816: N +Case #817: N +Case #818: N +Case #819: Y +Case #820: Y +Case #821: N +Case #822: Y +Case #823: N +Case #824: N +Case #825: N +Case #826: N +Case #827: N +Case #828: Y +Case #829: N +Case #830: N +Case #831: N +Case #832: N +Case #833: N +Case #834: N +Case #835: N +Case #836: Y +Case #837: N +Case #838: Y +Case #839: Y +Case #840: N +Case #841: N +Case #842: Y +Case #843: N +Case #844: N +Case #845: Y +Case #846: N +Case #847: Y +Case #848: N +Case #849: Y +Case #850: N +Case #851: N +Case #852: N +Case #853: N +Case #854: N +Case #855: N +Case #856: N +Case #857: N +Case #858: N +Case #859: N +Case #860: Y +Case #861: N +Case #862: N +Case #863: Y +Case #864: Y +Case #865: N +Case #866: N +Case #867: N +Case #868: N +Case #869: Y +Case #870: N +Case #871: N +Case #872: N +Case #873: N +Case #874: N +Case #875: N +Case #876: N +Case #877: N +Case #878: N +Case #879: N +Case #880: N +Case #881: N +Case #882: N +Case #883: Y +Case #884: N +Case #885: N +Case #886: N +Case #887: N +Case #888: Y +Case #889: N +Case #890: N +Case #891: N +Case #892: N +Case #893: N +Case #894: Y +Case #895: N +Case #896: N +Case #897: N +Case #898: N +Case #899: N +Case #900: N +Case #901: N +Case #902: N +Case #903: N +Case #904: Y +Case #905: N +Case #906: N +Case #907: Y +Case #908: Y +Case #909: N +Case #910: N +Case #911: N +Case #912: N +Case #913: N +Case #914: N +Case #915: Y +Case #916: Y +Case #917: N +Case #918: N +Case #919: Y +Case #920: N +Case #921: Y +Case #922: N +Case #923: Y +Case #924: N +Case #925: N +Case #926: N +Case #927: N +Case #928: Y +Case #929: N +Case #930: N +Case #931: N +Case #932: Y +Case #933: N +Case #934: N +Case #935: Y +Case #936: N +Case #937: N +Case #938: N +Case #939: N +Case #940: N +Case #941: N +Case #942: N +Case #943: Y +Case #944: Y +Case #945: Y +Case #946: N +Case #947: N +Case #948: N +Case #949: Y +Case #950: Y +Case #951: N +Case #952: N +Case #953: N +Case #954: N +Case #955: N +Case #956: Y +Case #957: Y +Case #958: N +Case #959: N +Case #960: N +Case #961: N +Case #962: N +Case #963: N +Case #964: N +Case #965: N +Case #966: Y +Case #967: Y +Case #968: Y +Case #969: N +Case #970: N +Case #971: N +Case #972: N +Case #973: N +Case #974: N +Case #975: N +Case #976: N +Case #977: N +Case #978: N +Case #979: N +Case #980: N +Case #981: N +Case #982: N +Case #983: N +Case #984: N +Case #985: N +Case #986: N +Case #987: N +Case #988: N +Case #989: N +Case #990: N +Case #991: N +Case #992: N +Case #993: Y +Case #994: Y +Case #995: Y +Case #996: N +Case #997: N +Case #998: N +Case #999: N +Case #1000: Y +Case #1001: N +Case #1002: N +Case #1003: Y +Case #1004: N +Case #1005: N +Case #1006: N +Case #1007: Y +Case #1008: N +Case #1009: N +Case #1010: N +Case #1011: N +Case #1012: N +Case #1013: N +Case #1014: Y +Case #1015: N +Case #1016: N +Case #1017: Y +Case #1018: N diff --git a/2019/round2/seafood.cpp b/2019/round2/seafood.cpp new file mode 100644 index 0000000000000000000000000000000000000000..d011e9d6ff22b4b8d3935575619a23126c4bca20 --- /dev/null +++ b/2019/round2/seafood.cpp @@ -0,0 +1,196 @@ +// Seafood +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +#define LIM 800001 + +int N,K; +int G[2][LIM]; +char O[LIM]; +pair< int, pair > P[LIM]; +int C[LIM],B[LIM]; +int sufCB[LIM],sufCH[LIM]; +int ss,nfr; +PR st[LIM],fr[LIM]; + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int i,j,a,b,c,d,p; + LL ans; + // testcase loop + Read(T); + Fox1(t,T) + { + // input, and generate values + Read(N); + Fox(i,2) + { + Read(G[i][0]),Read(G[i][1]),Read(a),Read(b),Read(c),Read(d); + FoxI(j,2,N-1) + G[i][j]=((LL)a*G[i][j-2] + (LL)b*G[i][j-1] + c)%d+1; + } + scanf("%s",&O); + Fox(i,N) + P[i]=mp(G[0][i],mp(O[i],G[1][i])); + // sort objects by position + sort(P,P+N); + // get list of clams + K=0; + Fox(i,N) + if (P[i].y.x=='C') + C[K++]=i; + // get list of useful rocks up to final clam + ss=0; + FoxR(i,C[K-1]) + if ((P[i].y.x=='R') && ((!ss) || (P[i].y.y>st[ss-1].x))) + st[ss++]=mp(P[i].y.y,P[i].x); + // get clams' backtrack positions + Fill(B,-1); + Fox(i,K) + { + j=lower_bound(st,st+ss,mp(P[C[i]].y.y+1,0))-st; + if (j==ss) + break; + B[i]=st[j].y; + } + // precompute suffix mins/maxes of clams' backtrack positions/hardnesses + sufCB[K]=INF,sufCH[K]=0; + FoxR(i,K) + { + sufCB[i]=min(sufCB[i+1],B[i]); + sufCH[i]=max(sufCH[i+1],P[C[i]].y.y); + } + // get list of useful rocks past final clam + nfr=0; + FoxI(i,C[K-1]+1,N-1) + if ((!nfr) || (P[i].y.y>fr[nfr-1].x)) + fr[nfr++]=mp(P[i].y.y,P[i].x); + // DP + ans=2*INF; + ss=0; + Fox(i,K) + { + // perform optional transition from an earlier clam + if (!i) + d=0; + else + { + p=P[C[i-1]].x; + while (ss>1) + { + a=st[ss-1].y; + b=min(a,st[ss-2].y); + if ((LL)st[ss-1].x+2*max(0,p-a)<(LL)st[ss-2].x+2*max(0,p-b)) + break; + st[ss-2].y=b; + ss--; + } + d=st[ss-1].x+2*max(0,p-st[ss-1].y); + } + st[ss++]=mp(d,B[i]); + // consider concluding with transition to final clam + p=P[C[K-1]].x; + if (sufCB[i]>=0) + Min(ans,(LL)d+max(0,p-sufCB[i])); + a=lower_bound(fr,fr+nfr,mp(sufCH[i]+1,0))-fr; + if (a +Percy is a harlequin tuskfish who lives on a stretch of the sea floor, which may be represented as a number line. +There are N objects resting on the sand beneath the waves, the ith of which is at a positive integral position Pi, +is either a clam (if Oi = "C") or otherwise a rock (if Oi = "R"), +and in either case has a hardness of Hi. No two objects are at the same position, and at least one of the objects is a clam. +

+ +

+Percy initially finds himself at position 0, and can then swim in either direction along the number line at a rate of 1 unit per second. +Whenever he occupies the same position as a clam, he may pick it up and begin carrying it around in his mouth. +Picking up a clam requires no additional time, and Percy is talented enough to carry any number of clams at once. +

+ +

+Percy would like to devour the delicious interior of each clam, but can't get to it without first somehow breaking open its hard shell. +Fortunately, Percy is clever and persistent enough to have a solution to this problem. +Whenever he occupies the same position as a rock, he may take each clam that he's currently carrying that has a strictly smaller hardness than that of the rock, +knock the clam against the rock to break open its shell, and eat the meal packaged within! This process requires no additional time per clam. +

+ +

+What's the minimum amount of time required for Percy to swim around and eat all of the clams (by picking each one up and then knocking it against a harder rock than itself), if at all possible? +

+ +

+In order to reduce the size of the input, the object's positions and hardnesses will not all be provided explicitly. +Instead, you'll be given P1, P2, H1, H2, +as well as the 8 constants Ap, Bp, Cp, Dp, +Ah, Bh, Ch, and Dh, +and must then compute P3..N and H3..N as follows (bearing in mind that intermediate values may not fit within 32-bit integers): +

+ +

+Pi = ((Ap * Pi-2 ++ Bp * Pi-1 + Cp) modulo Dp) + 1, +for i = 3 to N. +

+ +

+Hi = ((Ah * Hi-2 ++ Bh * Hi-1 + Ch) modulo Dh) + 1, +for i = 3 to N. +

+ + + +

Input

+ +

+Input begins with an integer T, the number of days Percy goes hunting for clams. +For each day, there are four lines. +The first line contains the integer N. +The second line contains the space-separated integers P1, P2, +Ap, Bp, Cp, and Dp. +The third line contains the space-separated integers H1, H2, +Ah, Bh, Ch, and Dh. +The fourth line contains the length-N string O1..N. +

+ + +

Output

+ +

+For the ith day, print a line containing "Case #i: " followed by one integer, +either the minimum number of seconds required for Percy to break open and eat all of the clams, or -1 if he cannot do so. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 250
+2 ≤ N ≤ 800,000
+0 ≤ Ap, Bp, Cp, +Ah, Bh, Ch ≤ 1,000,000,000
+1 ≤ Dp, Dh ≤ 1,000,000,000
+1 ≤ PiDp
+1 ≤ HiDh
+

+ + +

Explanation of Sample

+ +

+In the first case, P = [5, 10] and H = [30, 31]. Percy should swim to position 5, pick up the clam with hardness 30, swim onwards to position 10, +and break open the clam on the rock with hardness 31. +

+ +

+In the second case, P = [5, 10] and H = [31, 30]. Percy should now swim to position 10 to pick up the clam, and then back to position 5 to break it open. +

+ +

+In the third case, P = [5, 10] and H = [30, 30]. Once Percy picks up the clam, no rock harder than it exists on the sea floor, meaning that he can never break it open. +

+ +

+In the fourth case, P = [10, 50, 11, 52] and H = [50, 10, 49, 8]. +

+ +

+In the fifth case, P = [415, 711, 225, 136, 256, 469, 714, 399, 841, 697, 480, 147, 98, 837, 745, 660, 44, 226, 73, 7] and H = [9, 2, 10, 6, 6, 2, 7, 13, 4, 5, 11, 11, 4, 3, 7, 1, 6, 10, 10, 1]. +

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281715200 295372774 201849952 10096460 974620500 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+263 +168978783 1741277 622593187 898856637 64995848 213280330 +18503541 38081452 203505126 216118099 835041287 46628095 +CRCRRRRRRCCCRCCCRRCRRRRCCRRRRRRRCCRCRRRCCCCRRCCRRCRRCRCCCRCCRCCRCCRCCRRCCCCRRCCRCCCCRCCCRCCCRRCRRRCRCCRRRCRRRRCRCRCCCRCRCRCRRCRRRCCRCCRRRRRRCCCCCCCRRRCCCRCCCRRCCCCRRRCCRCCRCRRRCRCRCCRCCCCCRCRCCRRCRRCRCRRCRCCRRCCRCRRCRCCRRRCRRRCCRCCRRCCRCCCRCRCCRCCCCRCRCCRRRRRRRRR +74 +90478522 284782185 372518515 822096623 305456289 549203902 +39861706 648487669 738358596 430684083 721776008 861195092 +RCRCRRCRRRRRRRRRRRRRCRRRRCRCRCRCRRRRCRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR +424 +70558 353473717 644905060 974314901 325902650 783612470 +191944471 173989240 352859093 636816860 665204449 238898747 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+971 +463049916 224626174 125223454 8744185 300069825 962630920 +27895744 308662955 454716721 580369750 791860066 342556143 +CCCCCCCCRCCCRCCCCCRRCRCCRCRCCCRCCCCCCRCCCCCCCCCRCCCRCCCRCCCCCCCCRCCRCRCCRCRRRCCCRCCRCCCCCCCCRCRCCCRRCCCRCCCCCCCRCCCCCCCRCCCRRRCCCCCCCRCCCCCCCCRCCCRRCCCCCCCCCCCCRCRCCCCCCCCCCCCCCCCCCCRCCCCCCRCCCCCRRRCCCCRCCCCCRCCCCCCCRRCCCCCCCCCCCCRRRRCCCCCCCRCCCCRCRCRCRCCCRCCCCCCCCRCRRCRRRRCCCCRCCCRCCRCCCCCCCCRCRCCCRRCCCRCRCCCCCCRCCCCCCRCCCCCCRCCCCCCCCCCCRCCCCCCCCCCRCCRCCCCCCCCCCCCCCCCCRCCCCCCCRCCCCCCCRCCRCRRCCCCCCCCCCCCCCCCCRCCCCCCCCCCRRCCCCCRCCCCCRCCCCCCCCCCCCCCRCCCCCCCRCCCCCRRRRCRCCCRRCCCCRCCCCCCCCRCRCCCCCCCCCRCCCCCCCCCRCCCCCRCRCCCCCRCRCCCRCCCCCRCCCCCCCRRRRCCCRCCRCCCCCCRCCCCCCCCCCRCRCCCCCRRCCCRCRRCRCRCCRCCCCCCCCCCCCCCCCCRCCCCRCCCRRCCCCRRCCCCRCCCRCCCRCCCCRCCCCCRRCCCRRCCCCCCCCCRCCRCRRCCCCRCCCCRRCCCCCCCCCCCCCCCCRCCCRCCCCCRCCCCCCCCCRCCCRCCCCCCRRCCCCCCCRCCCCCRRCCCCRRCRRCCRCCRCCCCCCCCCCCCCCCCCCCCRCRCCCCCCRCCCCCCCCRCCRCCCCRCCCCCCCCCCCCCCCCCCCCCCCCCCRCCCRCRCRCCCCCCCCCCCRCCRCRCCCCRCRCCCCCRCCCCCCCCCCCCCCRCCCCCCRCCCCRCCRCCCCCCCCCRCRCCCCCCCCRCCCRCRRCCCCCCRCCCCCRCCCRCCRCRCCCCCCCCRRCC +710 +268247914 18649114 698025053 18919748 660045396 427203635 +159227384 414369887 431550137 210249318 22274917 491821499 +RCRCCCRCRCCRRRRRRCCRCRCRRRCCRRCCRCCRRRCRCRCCRRCRCRCCRRRCRRCRCRRRRRRCCCRRRCRRRCCCCRRCCCCRCCCCCRRRRRRCRCCCRRRRCRCCCCRRRRRRCCRRRCRCCRRCCCRCCCCCRCRCCCCCCRCRRCCCCCCRRCCRRCCRCCCCRRCRCRCRCCCRRRRRCRRRRCCCRCCRCRCCRCRRRCRRCCRCRCRRRRCCCCRCCCCCRCCRCRRRCCRCCRRRRCRCRCCRCRCRRRRCCRCCCCCCCRRRRCCCRCCCRCRCRCCRRCCCRCRCCCRRCRCCCRCRCRRRRCCCCRRCCCCRCCRCCCRCRCRCCCCCCCRCRCRRRRCRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR +660 +279141941 28542623 441513628 991135777 950756329 370284430 +189740473 707865086 134022412 704550160 890918711 936829619 +CCCRCCCRCCCCCRCCCCCCCCCCCCCCCCCCCCRCCCCCCCCCCCCRCCCCCCRCCCCCCCRCCCCCCCCRCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCRRCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCRCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCRCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCRCCCCCCCRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR +979 +515846188 215209620 299528238 857715764 46300068 708210195 +9343660 218062580 255245421 67368164 450556977 519975215 +RRRRRRRCRCRRCCRRRRRRRRRRCRRRRCRRRRRRCRRCCRCRCRCRRRRRRRCRRCCRCCRRRRRCCRCRRRRRRRRRRRRRRRRRRRRCRRRRRRCCRRRRRRRRRRRRRCRRRCRCRCRCRRRRRRRCRRRRRRRCRCRRRCCRCRRRRRRCRRRRCRRRRRRRCRRRRCCRRRRRRRRRRRCCRCRRRRCCCCRRRCRRRRCCRRRRRRRRRCRRRRRRRCRRRRCRRRRRRRRRRCCRRRRRCRRRRRRCCCRRRRCRRCRCRRCCRRRCRRCRRCRCRCRRRRRRRCCRRRRRRRRRRRRRRCCCRRRRRRRRRRCRCRCRRRRCRCRRRRRRRRRRRCCRRRRRRCRRRCRRCRRRRRRRRCRRRRRRRCRRRRRRCRRRRRRRRCRRRCRRRRRRRRRRRRRCRRRRCRRRRRRRRRCRCRRRRRRRRRRCRRCRRRRRRRRRCCRRRCRRRRRRRRRCRCRRRRRRRRRCRRRRCRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR +300 +142605302 329760463 229039986 496988094 658401285 561804373 +272046433 34480634 294091635 626134666 804653203 290209220 +CCCCCRCCCCRRCRCCCCCRRCCRCRRCCRCCCCRCRRCRCCRRCCCRRCCRCCCCCRRCRCCCCCCCCCCRCCCRCCRCCCCRCRRRCCCCCRCCCCCRCCCCCCCRCCCCCCCCCCCRCCRRCCRCCCCCCCRCCCRCCRCCRCCCCCCCCCCCCCCCRRRCCRCCRCCRCCCCRCCCCRRCRCCCCCCRCCCRCCCRCCCCRCRCCCCCRRCCRCCCCCRCCRCCCCCCRCCCRCCCCRCCCCCCCCCCCCCCCCCCRCCCCCCRCCRCCCRCRCCCCCRCRCCRCCCCCRCRCCCR diff --git a/2019/round2/seafood.md b/2019/round2/seafood.md new file mode 100644 index 0000000000000000000000000000000000000000..070ee198504776574b39a56368ed71f4f84eec19 --- /dev/null +++ b/2019/round2/seafood.md @@ -0,0 +1,81 @@ +Percy is a harlequin tuskfish who lives on a stretch of the sea floor, which +may be represented as a number line. There are **N** objects resting on the +sand beneath the waves, the _i_th of which is at a positive integral position +**Pi**, is either a clam (if **Oi** = "C") or otherwise a rock (if **Oi** = +"R"), and in either case has a hardness of **Hi**. No two objects are at the +same position, and at least one of the objects is a clam. + +Percy initially finds himself at position 0, and can then swim in either +direction along the number line at a rate of 1 unit per second. Whenever he +occupies the same position as a clam, he may pick it up and begin carrying it +around in his mouth. Picking up a clam requires no additional time, and Percy +is talented enough to carry any number of clams at once. + +Percy would like to devour the delicious interior of each clam, but can't get +to it without first somehow breaking open its hard shell. Fortunately, Percy +is clever and persistent enough to have a +[solution](https://www.radiotimes.com/news/2018-01-26/blue-planet-2-fish- +clams-tools/) to this problem. Whenever he occupies the same position as a +rock, he may take each clam that he's currently carrying that has a strictly +smaller hardness than that of the rock, knock the clam against the rock to +break open its shell, and eat the meal packaged within! This process requires +no additional time per clam. + +What's the minimum amount of time required for Percy to swim around and eat +all of the clams (by picking each one up and then knocking it against a harder +rock than itself), if at all possible? + +In order to reduce the size of the input, the object's positions and +hardnesses will not all be provided explicitly. Instead, you'll be given +**P1**, **P2**, **H1**, **H2**, as well as the 8 constants **Ap**, **Bp**, +**Cp**, **Dp**, **Ah**, **Bh**, **Ch**, and **Dh**, and must then compute +**P3..N** and **H3..N** as follows (bearing in mind that intermediate values +may not fit within 32-bit integers): + +**Pi** = ((**Ap** * **Pi-2** \+ **Bp** * **Pi-1** \+ **Cp**) modulo **Dp**) + 1, for _i_ = 3 to **N**. + +**Hi** = ((**Ah** * **Hi-2** \+ **Bh** * **Hi-1** \+ **Ch**) modulo **Dh**) + 1, for _i_ = 3 to **N**. + +### Input + +Input begins with an integer **T**, the number of days Percy goes hunting for +clams. For each day, there are four lines. The first line contains the integer +**N**. The second line contains the space-separated integers **P1**, **P2**, +**Ap**, **Bp**, **Cp**, and **Dp**. The third line contains the space- +separated integers **H1**, **H2**, **Ah**, **Bh**, **Ch**, and **Dh**. The +fourth line contains the length-**N** string **O1..N**. + +### Output + +For the _i_th day, print a line containing "Case #_i_: " followed by one +integer, either the minimum number of seconds required for Percy to break open +and eat all of the clams, or -1 if he cannot do so. + +### Constraints + +1 ≤ **T** ≤ 250 +2 ≤ **N** ≤ 800,000 +0 ≤ **Ap**, **Bp**, **Cp**, **Ah**, **Bh**, **Ch** ≤ 1,000,000,000 +1 ≤ **Dp**, **Dh** ≤ 1,000,000,000 +1 ≤ **Pi** ≤ **Dp** +1 ≤ **Hi** ≤ **Dh** + +### Explanation of Sample + +In the first case, P = [5, 10] and H = [30, 31]. Percy should swim to position +5, pick up the clam with hardness 30, swim onwards to position 10, and break +open the clam on the rock with hardness 31. + +In the second case, P = [5, 10] and H = [31, 30]. Percy should now swim to +position 10 to pick up the clam, and then back to position 5 to break it open. + +In the third case, P = [5, 10] and H = [30, 30]. Once Percy picks up the clam, +no rock harder than it exists on the sea floor, meaning that he can never +break it open. + +In the fourth case, P = [10, 50, 11, 52] and H = [50, 10, 49, 8]. + +In the fifth case, P = [415, 711, 225, 136, 256, 469, 714, 399, 841, 697, 480, +147, 98, 837, 745, 660, 44, 226, 73, 7] and H = [9, 2, 10, 6, 6, 2, 7, 13, 4, +5, 11, 11, 4, 3, 7, 1, 6, 10, 10, 1]. + diff --git a/2019/round2/seafood.out b/2019/round2/seafood.out new file mode 100644 index 0000000000000000000000000000000000000000..b1a35a0cebd8bc71b25f0e25ecff95ef00a098f7 --- /dev/null +++ b/2019/round2/seafood.out @@ -0,0 +1,518 @@ +Case #1: 10 +Case #2: 15 +Case #3: -1 +Case #4: 56 +Case #5: 1099 +Case #6: 890508817 +Case #7: 88 +Case #8: 727993475 +Case #9: -1 +Case #10: 164 +Case #11: 36800167 +Case #12: 34005546 +Case #13: 23335761 +Case #14: 39570465 +Case #15: 1433979863 +Case #16: 54042277 +Case #17: 684662534 +Case #18: 118297341 +Case #19: 54326613 +Case #20: 1094799757 +Case #21: -1 +Case 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b/2019/round3/984673281988054.jpg @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9a4687e7dea6db92db3d0f506f2c394f1c16bd990d3da53136034d87dd71b695 +size 15838 diff --git a/2019/round3/chain_of_command.cpp b/2019/round3/chain_of_command.cpp new file mode 100644 index 0000000000000000000000000000000000000000..7bcbc73d08f9b0caac2a27fb58903116f2194524 --- /dev/null +++ b/2019/round3/chain_of_command.cpp @@ -0,0 +1,241 @@ +// Chain of Command +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +#define LIM 800001 +#define MOD 1000000007 + +int N; +LL curSum; +int ind,sz[LIM],in[LIM],out[LIM],nxt[LIM]; +int C[LIM],S[LIM]; +int BLT[2][LIM]; // 0: B, 1: X +bool X[LIM],hasSetXUpward[LIM]; +vector ch[LIM],unsetXch[LIM]; + +void RecCalcSz(int i) +{ + int j; + sz[i]=1; + Fox(j,Sz(ch[i])) + { + int c=ch[i][j]; + RecCalcSz(c); + sz[i]+=sz[c]; + if(sz[c]>sz[ch[i][0]]) + swap(ch[i][0],ch[i][j]); + } +} + +void RecHLD(int i) +{ + in[i]=ind++; + int j; + Fox(j,Sz(ch[i])) + { + int c=ch[i][j]; + nxt[c]=j ? c : nxt[i]; + RecHLD(c); + } + out[i]=ind; +} + +void IncBLT(int b,int i) +{ + for (i++; i<=N; i+=(i&-i)) + BLT[b][i]++; +} + +int QueryBLT(int b,int i) +{ + int s=0; + for (i++; i>0; i-=(i&-i)) + s+=BLT[b][i]; + return(s); +} + +int QueryBInSubtree(int i) +{ + return(QueryBLT(0,out[i]-1)-QueryBLT(0,in[i]-1)); +} + +int QueryXToRoot(int i) +{ + int x=1; + while (i>=0) + { + int a=nxt[i]; + x+=QueryBLT(1,in[i])-QueryBLT(1,in[a]-1); + i=C[a]; + } + return(x); +} + +void SetX(int i) +{ + if (X[i]) + return; + X[i]=1; + IncBLT(1,in[i]); + curSum+=QueryBInSubtree(i); +} + +void Bribe(int i) +{ + int j; + IncBLT(0,in[i]); + curSum+=QueryXToRoot(i); + Fox(j,Sz(ch[i])) + SetX(ch[i][j]); + for(;;) + { + if (hasSetXUpward[i]) + break; + hasSetXUpward[i]=1; + int c=C[i]; + if (c<0) + break; + Fox(j,Sz(unsetXch[c])) + if (unsetXch[c][j]!=i) + SetX(unsetXch[c][j]); + unsetXch[c].clear(); + unsetXch[c].pb(i); + i=c; + } +} + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int i,r; + // testcase loop + Read(T); + Fox1(t,T) + { + // init + Fox(i,N) + { + ch[i].clear(); + unsetXch[i].clear(); + } + // input + Read(N); + Fox(i,N) + { + Read(C[i]),C[i]--; + if (C[i]<0) + r=i; + else + { + ch[C[i]].pb(i); + unsetXch[C[i]].pb(i); + } + } + // perform heavy-light decomposition + ind=0; + RecCalcSz(r); + nxt[r]=r; + RecHLD(r); + // init + curSum=0; + Fill(BLT,0); + Fill(X,0); + Fill(hasSetXUpward,0); + // process bribes + int ans=1; + Fox(i,N) + { + Bribe(i); + ans=ans*(curSum%MOD)%MOD; + } + // output + printf("Case #%d: %d\n",t,ans); + } + return(0); +} \ No newline at end of file diff --git a/2019/round3/chain_of_command.html b/2019/round3/chain_of_command.html new file mode 100644 index 0000000000000000000000000000000000000000..43afc1f4d5078c374490d71a8e74e3037143d7ff --- /dev/null +++ b/2019/round3/chain_of_command.html @@ -0,0 +1,98 @@ +

+At last, Mr. X has managed to return to the school at which he formerly taught, with the intention of confronting his suspicious successor, Mr. Y. +However, it appears that Mr. Y has fortified his position — he has brainwashed all of his students into believing that he's the world's best teacher +through the timeless ploy of replacing classes with extra recesses. There's no way that Mr. Y can be thrown out of the school without first compromising his students' support! +

+ +

+There are N students in Mr. Y's class, with IDs from 1 to N. In an attempt to maximize security, Mr. Y has arranged them into a hierarchical structure, +with each student i either reporting to a commanding student Ci, or not reporting to any other student +(indicated by Ci = 0). There's exactly one student i for whom Ci = 0, who is the class leader. +

+ +

+A chain of command is a sequence of one or more students going up the hierarchical structure starting from some student i and ending somewhere between +i and the class leader (inclusive): iCiCCi → etc. +It's guaranteed that, for each student i, there exists a chain of command beginning at them and ending at the class leader. +

+ +

+Initially, all N students are under Mr. Y's control. However, Mr. X is about to perform some bribery of his own. One by one, in order from 1 to N, +Mr. X will bribe each student with healthy snacks. After the first b bribes, students 1..b will be under Mr. X's control instead of Mr. Y's. +

+ +

+After each of the N bribes, Mr. X would like to evaluate the vulnerability of Mr. Y's class to a potential takeover. +To do so, he'll determine N hypothetical values: +for each student i, he'll compute the maximum length that a controlled chain beginning with student i could possibly have if 0 or more promotions +were to first take place (or 0 if no such chain could exist). +

+ +

+A controlled chain is a chain of command consisting exclusively of students under Mr. X's control. A promotion is a modification to the class structure +in which Mr. X selects a certain student j with a commanding student c = Cj +(such that c ≠ 0 and ci), expels student c (removing them from the class entirely), and brings j +up to occupy c's former place (setting Cj to Cc, +and for each other student k such that Ck = c, now setting Ck to j). +Note that each of these hypothetical values should be considered independently of the others; Mr. X will never actually perform any promotions and permanently alter the class structure. +

+ +

+In order to reduce the size of the output, these N2 values should be aggregated into a single integer as follows: +Letting Sb be the sum of the N students' maximum controlled chain lengths after the first b students have been bribed, +output (S1 * S2 * ... * SN) modulo 1,000,000,007. +

+ + +

Input

+ +

+Input begins with an integer T, the number of times Mr. X needs to wrest control from Mr. Y. +For each time, there is first a line containing the integer N. +Then, N lines follow, the ith of which contains the integer Ci. +

+ + +

Output

+ +

+For the ith time, print a line containing "Case #i: " +followed by a single integer, the product of all N sums of maximum controlled chain lengths, modulo 1,000,000,007. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 80
+1 ≤ N ≤ 800,000
+0 ≤ CiN
+

+ + +

Explanation of Sample

+ +

+In the first case, after the first student has been bribed, a length-1 controlled chain can begin at student 1, while no controlled chain can begin at student 2. +Once the second student has also been bribed, a length-1 controlled chain can still begin at student 1, while a length-2 controlled chain +may now begin at student 2 (2 → 1). This results in a total answer of (1 + 0) * (1 + 2) = 3 (modulo 1,000,000,007). +

+ +

+In the second case, after the first two students have been bribed, a length-2 controlled chain can begin at student 1 (1 → 2) if student 1 gets promoted (replacing student 3). +The total answer comes out to (1 + 0 + 0) * (2 + 1 + 0) * (3 + 1 + 2) = 18 (modulo 1,000,000,007). +

+ +

+In the third case, after the first two students have been bribed, a length-2 controlled chain may begin at student 1 (1 → 2) if student 2 gets promoted (replacing student 3), +and a length-1 controlled chain can similarly begin at student 2 (2 → 1) if student 1 gets promoted (replacing student 3). +The total answer comes out to (1 + 0 + 0) * (2 + 2 + 0) * (2 + 2 + 1) = 20 (modulo 1,000,000,007). + + +

+In the fourth case, the total answer is (1 + 0 + 0 + 0 + 0) * (2 + 2 + 0 + 0 + 0) * (2 + 3 + 2 + 0 + 0) * (2 + 3 + 2 + 1 + 0) * (2 + 3 + 2 + 1 + 3) = 2464 (modulo 1,000,000,007). +

+ +

+In the fifth case, the total answer is 1 * 3 * 7 * 11 * 14 * 16 * 20 * 28 * 33 * 39 * 44 * 47 = 790446393 (modulo 1,000,000,007). +

diff --git a/2019/round3/chain_of_command.in b/2019/round3/chain_of_command.in new file mode 100644 index 0000000000000000000000000000000000000000..ad5e5f17d88851d698f96cd4d924da62e2fd499e --- /dev/null +++ b/2019/round3/chain_of_command.in @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6997c0c5913007e67cc6c498cc9fd13994ea0a207e4ee17c12fca42b8788c3bf +size 23990935 diff --git a/2019/round3/chain_of_command.md b/2019/round3/chain_of_command.md new file mode 100644 index 0000000000000000000000000000000000000000..9928c844031d87b9b0db989f24e3fbb17be0b088 --- /dev/null +++ b/2019/round3/chain_of_command.md @@ -0,0 +1,96 @@ +At last, Mr. X has managed to return to the school at which he formerly +taught, with the intention of confronting his suspicious successor, Mr. Y. +However, it appears that Mr. Y has fortified his position — he has brainwashed +all of his students into believing that he's the world's best teacher through +the timeless ploy of replacing classes with extra recesses. There's no way +that Mr. Y can be thrown out of the school without first compromising his +students' support! + +There are **N** students in Mr. Y's class, with IDs from 1 to **N**. In an +attempt to maximize security, Mr. Y has arranged them into a hierarchical +structure, with each student _i_ either reporting to a commanding student +**Ci**, or not reporting to any other student (indicated by **Ci** = 0). +There's exactly one student _i_ for whom **Ci** = 0, who is the class leader. + +A _chain of command_ is a sequence of one or more students going up the +hierarchical structure starting from some student _i_ and ending somewhere +between _i_ and the class leader (inclusive): _i_ → **Ci** → **CCi** → etc. +It's guaranteed that, for each student _i_, there exists a _chain of command_ +beginning at them and ending at the class leader. + +Initially, all **N** students are under Mr. Y's control. However, Mr. X is +about to perform some bribery of his own. One by one, in order from 1 to +**N**, Mr. X will bribe each student with healthy snacks. After the first _b_ +bribes, students 1.._b_ will be under Mr. X's control instead of Mr. Y's. + +After each of the **N** bribes, Mr. X would like to evaluate the vulnerability +of Mr. Y's class to a potential takeover. To do so, he'll determine **N** +hypothetical values: for each student _i_, he'll compute the maximum length +that a _controlled chain_ beginning with student _i_ could possibly have if 0 +or more _promotions_ were to first take place (or 0 if no such chain could +exist). + +A _controlled chain_ is a _chain of command_ consisting exclusively of +students under Mr. X's control. A _promotion_ is a modification to the class +structure in which Mr. X selects a certain student _j_ with a commanding +student _c_ = **Cj** (such that _c_ ≠ 0 and _c_ ≠ _i_), expels student _c_ +(removing them from the class entirely), and brings _j_ up to occupy _c_'s +former place (setting **Cj** to **Cc**, and for each other student _k_ such +that **Ck** = _c_, now setting **Ck** to j). Note that each of these +hypothetical values should be considered independently of the others; Mr. X +will never actually perform any _promotions_ and permanently alter the class +structure. + +In order to reduce the size of the output, these **N2** values should be +aggregated into a single integer as follows: Letting **Sb** be the sum of the +**N** students' maximum _controlled chain_ lengths after the first _b_ +students have been bribed, output (**S1** * **S2** * ... * **SN**) modulo +1,000,000,007. + +### Input + +Input begins with an integer **T**, the number of times Mr. X needs to wrest +control from Mr. Y. For each time, there is first a line containing the +integer **N**. Then, **N** lines follow, the _i_th of which contains the +integer **Ci**. + +### Output + +For the _i_th time, print a line containing "Case #_i_: " followed by a single +integer, the product of all **N** sums of maximum _controlled chain_ lengths, +modulo 1,000,000,007. + +### Constraints + +1 ≤ **T** ≤ 80 +1 ≤ **N** ≤ 800,000 +0 ≤ **Ci** ≤ **N** + +### Explanation of Sample + +In the first case, after the first student has been bribed, a length-1 +_controlled chain_ can begin at student 1, while no _controlled chain_ can +begin at student 2. Once the second student has also been bribed, a length-1 +_controlled chain_ can still begin at student 1, while a length-2 _controlled +chain_ may now begin at student 2 (2 → 1). This results in a total answer of +(1 + 0) * (1 + 2) = 3 (modulo 1,000,000,007). + +In the second case, after the first two students have been bribed, a length-2 +_controlled chain_ can begin at student 1 (1 → 2) if student 1 gets promoted +(replacing student 3). The total answer comes out to (1 + 0 + 0) * (2 + 1 + 0) +* (3 + 1 + 2) = 18 (modulo 1,000,000,007). + +In the third case, after the first two students have been bribed, a length-2 +_controlled chain_ may begin at student 1 (1 → 2) if student 2 gets promoted +(replacing student 3), and a length-1 _controlled chain_ can similarly begin +at student 2 (2 → 1) if student 1 gets promoted (replacing student 3). The +total answer comes out to (1 + 0 + 0) * (2 + 2 + 0) * (2 + 2 + 1) = 20 (modulo +1,000,000,007). _ + +In the fourth case, the total answer is (1 + 0 + 0 + 0 + 0) * (2 + 2 + 0 + 0 + +0) * (2 + 3 + 2 + 0 + 0) * (2 + 3 + 2 + 1 + 0) * (2 + 3 + 2 + 1 + 3) = 2464 +(modulo 1,000,000,007). + +In the fifth case, the total answer is 1 * 3 * 7 * 11 * 14 * 16 * 20 * 28 * 33 +* 39 * 44 * 47 = 790446393 (modulo 1,000,000,007). + diff --git a/2019/round3/chain_of_command.out b/2019/round3/chain_of_command.out new file mode 100644 index 0000000000000000000000000000000000000000..acd715997d1f36280a709474f5af163b47069358 --- /dev/null +++ b/2019/round3/chain_of_command.out @@ -0,0 +1,505 @@ +Case #1: 3 +Case #2: 18 +Case #3: 20 +Case #4: 2464 +Case #5: 790446393 +Case #6: 823296653 +Case #7: 519172640 +Case #8: 399091042 +Case #9: 177407671 +Case #10: 100358921 +Case #11: 822597280 +Case #12: 721096935 +Case #13: 910563926 +Case #14: 480344927 +Case #15: 916439114 +Case #16: 233263573 +Case #17: 319617065 +Case #18: 513996230 +Case #19: 2463621 +Case #20: 8765028 +Case #21: 322848340 +Case #22: 901004135 +Case #23: 646403154 +Case #24: 855464590 +Case #25: 885413711 +Case #26: 877199228 +Case #27: 827779724 +Case #28: 731691588 +Case #29: 730518448 +Case #30: 251152423 +Case #31: 164098313 +Case #32: 345086137 +Case #33: 735174732 +Case #34: 643792812 +Case #35: 238870242 +Case #36: 720103391 +Case #37: 670883111 +Case #38: 570436995 +Case #39: 269530244 +Case #40: 116058031 +Case #41: 356825978 +Case #42: 455183881 +Case #43: 796166228 +Case #44: 916131946 +Case #45: 49489561 +Case #46: 266820207 +Case #47: 265106788 +Case #48: 499900772 +Case #49: 875905003 +Case #50: 305199214 +Case #51: 148018528 +Case #52: 101311210 +Case #53: 348416952 +Case #54: 674603454 +Case #55: 361041516 +Case #56: 238747336 +Case #57: 488324902 +Case #58: 255287647 +Case #59: 952869269 +Case #60: 206119198 +Case #61: 825559331 +Case #62: 71770899 +Case #63: 553795432 +Case #64: 790166515 +Case #65: 620513070 +Case #66: 34860823 +Case #67: 422204299 +Case #68: 543011062 +Case #69: 626725336 +Case #70: 407410986 +Case #71: 116246679 +Case #72: 270944802 +Case #73: 662539438 +Case #74: 161986540 +Case #75: 402313109 +Case #76: 679728163 +Case #77: 153570345 +Case #78: 661356959 +Case #79: 577735961 +Case #80: 838228056 +Case #81: 442971069 +Case #82: 172746035 +Case #83: 457878444 +Case #84: 516018893 +Case #85: 671008132 +Case #86: 344920646 +Case #87: 885998101 +Case #88: 304728558 +Case #89: 104893534 +Case #90: 818655093 +Case #91: 246584600 +Case #92: 951734281 +Case #93: 445911539 +Case #94: 250815677 +Case #95: 712222465 +Case #96: 553751342 +Case #97: 304236580 +Case #98: 818233349 +Case #99: 83749508 +Case #100: 890171370 +Case #101: 956577242 +Case #102: 190536770 +Case #103: 864594833 +Case #104: 855690202 +Case #105: 886979104 +Case #106: 70822835 +Case #107: 899764158 +Case #108: 940759674 +Case #109: 481716438 +Case #110: 352247603 +Case #111: 461021961 +Case 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369611604 +Case #477: 668780927 +Case #478: 136657218 +Case #479: 218185319 +Case #480: 495314289 +Case #481: 654257293 +Case #482: 926112127 +Case #483: 495113166 +Case #484: 958047859 +Case #485: 358984351 +Case #486: 243226404 +Case #487: 858929348 +Case #488: 359860966 +Case #489: 986325850 +Case #490: 804912964 +Case #491: 859234448 +Case #492: 448606745 +Case #493: 248194310 +Case #494: 199989548 +Case #495: 791492311 +Case #496: 89199326 +Case #497: 866350363 +Case #498: 593275604 +Case #499: 462991862 +Case #500: 640560842 +Case #501: 193676128 +Case #502: 933528663 +Case #503: 822747929 +Case #504: 689912364 +Case #505: 572134597 diff --git a/2019/round3/integers_as_service.cpp b/2019/round3/integers_as_service.cpp new file mode 100644 index 0000000000000000000000000000000000000000..a3c3d8bf23aa29f3801fb5b1092914d5665c6173 --- /dev/null +++ b/2019/round3/integers_as_service.cpp @@ -0,0 +1,216 @@ +// Integers as a Service +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +#define LIM 2000 + +int N; +char O[LIM]; +int V[LIM],R[LIM]; +map minE,maxE,Fv,Fr; +map::iterator I; + +map Fact(int v) +{ + map F; + int p,e; + for (p=2; p*p<=v; p++) + { + e=0; + while (v%p==0) + v/=p,e++; + if (e) + F[p]=e; + } + if (v>1) + F[v]=1; + return(F); +} + +void SetMin(int p,int e) +{ + Max(minE[p],e); +} + +void SetMax(int p,int e) +{ + if (maxE.count(p)) + Min(maxE[p],e); + else + maxE[p]=e; +} + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int i,p,e,ev,er; + LL ans; + bool hasAP; + set AP; + set::iterator J,K; + // testcase loop + Read(T); + Fox1(t,T) + { + // init + printf("Case #%d: ",t); + minE.clear(),maxE.clear(); + hasAP=0; + // input + Read(N); + Fox(i,N) + scanf("%c%d%d\n",&O[i],&V[i],&R[i]); + // assemble prime exponent requirements based on original requirements + Fox(i,N) + { + Fv=Fact(V[i]),Fr=Fact(R[i]); + if (O[i]=='G') + { + if (V[i]%R[i]) + goto Imp; + Foxen(I,Fv) + { + p=I->x,ev=I->y; + er=Fr[p]; + SetMin(p,er); + if (ev>er) + SetMax(p,er); + } + } + else + { + if (R[i]%V[i]) + goto Imp; + Foxen(I,Fr) + { + p=I->x,er=I->y; + ev=Fv[p]; + SetMax(p,er); + if (evx); + } + else + for (J=AP.begin(); J!=AP.end();) + { + K=J,J++; + if (!Fr.count(*K)) + AP.erase(K); + } + } + } + // construct min. valid value of X + ans=1; + Foxen(I,minE) + { + p=I->x,e=I->y; + if ((e) && (hasAP) && (!AP.count(p))) + goto Imp; + if ((maxE.count(p)) && (maxE[p]INF) + goto Imp; + } + } + // output + printf("%lld\n",ans); + continue; +Imp:; + printf("-1\n"); + } + return(0); +} \ No newline at end of file diff --git a/2019/round3/integers_as_service.html b/2019/round3/integers_as_service.html new file mode 100644 index 0000000000000000000000000000000000000000..640c1de2f1e07c101087de7d635543def3235ac1 --- /dev/null +++ b/2019/round3/integers_as_service.html @@ -0,0 +1,83 @@ +

+Looking for a new direction for his company, Carlos wants to break into the most exciting tech field: digital rights management (DRM). +In the world of DRM, mega-corporations wage perpetual war against a vast sea of e-pirates, modern-day Robin Hoods of ambiguous moral character. +

+ +

+One of the biggest players in this struggle is Sony, the well-known copyrighter of numbers. Considering the speed with which Sony puts out new products, +it's no wonder they're having trouble coming up with enough secret encryption keys to protect all of their intellectual property. Enter Carlos. +

+ +

+ +"Gone are the days of paying over-priced number theory PhDs to craft primes by hand. I can make you a system that will generate all the numbers you need, +to your exact specifications." + +

+ +

+Sony wants to see a demonstration of Carlos's system before forking over millions of dollars in consultancy fees. They have some new products in development, +each of which requires a secret key, X. For each key, Sony has a list of N requirements. +The ith requirement has an operator character Oi, an integer value Vi, +and an integer result Ri. +

+ +

+When Oi is 'G', the ith requirement states that the greatest common divisor of +X and Vi must be Ri. That is, GCD(X, Vi) = Ri. +

+ +

+When Oi is 'L', the ith requirement states that the least common multiple of +X and Vi must be Ri. That is, LCM(X, Vi) = Ri. +

+ +

+There is also a global requirement that all of Sony's secret keys must be positive integers no larger than 1,000,000,000. +Help Carlos build any positive integer X consistent with all of these requirements, or determine that no such integer exists. +

+ + +

Input

+ +

+Input begins with an integer T, the number of secret keys that Sony wants Carlos to generate. +For each number, there is first a line containing the integer N. +Then, N lines follow, the ith of which contains the character Oi, +and the integers Vi and Ri, all separated by spaces. +

+ + +

Output

+ +

+For the ith secret key, print a line containing "Case #i: " +followed by a single integer: your chosen value of X, or -1 if no valid integer X exists. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 250
+1 ≤ N ≤ 2,000
+Oi ∈ {'G', 'L'}
+1 ≤ Vi, Ri ≤ 1,000,000,000
+

+ +

Explanation of Sample

+ +

+In the first case, GCD(6, 4) = 2, meaning that X = 6 satisfies the one and only requirement. +Note that, for this case and potentially other cases below, various other outputs will also be accepted. +

+ +

+In the second case, there exists no valid integer X such that 1 ≤ X ≤ 1,000,000,000 and LCM(X, 4) = 2. +

+ +

+In the third case, GCD(24, 18) = 6, LCM(24, 40) = 120, and GCD(24, 20) = 4, meaning that X = 24 is a valid choice. +

+ + diff --git a/2019/round3/integers_as_service.in b/2019/round3/integers_as_service.in new file mode 100644 index 0000000000000000000000000000000000000000..cbb280b99679f1b49adab6ed630c680b42898072 --- /dev/null +++ b/2019/round3/integers_as_service.in @@ -0,0 +1,30796 @@ +542 +1 +G 4 2 +1 +L 4 2 +3 +G 18 6 +L 40 120 +G 20 4 +3 +G 36 9 +L 10 90 +G 24 6 +4 +G 259904673 63 +L 42155313 885261573 +G 778065480 60597 +L 20448 963734688 +3 +G 3204696 72834 +G 1795435 4919 +G 3528270 3582 +2 +L 1000000000 1000000000 +G 1000000000 1000000000 +5 +L 589 334552 +G 3692 4 +L 955 542440 +L 82 23288 +L 574 163016 +15 +L 16640 881920 +G 676 4 +L 105470 6750080 +G 812 4 +L 666 11295360 +G 460 20 +L 8777 297715840 +G 293 1 +L 83 2815360 +G 2544 848 +L 427 14483840 +G 115 5 +L 588 4986240 +G 18 2 +L 607 20589440 +5 +G 50179535 1267 +L 24036257 697051453 +G 493636927 63133 +L 4334407 377093409 +G 747704303 5249 +24 +L 159 51198 +L 620 99820 +L 434 9982 +G 408 2 +L 791 36386 +L 820 132020 +G 425845 161 +G 88088 14 +L 524 84364 +L 396 63756 +G 1426 46 +L 258 41538 +L 839 270158 +L 432 69552 +L 706 113666 +L 544 87584 +L 933 300426 +L 753 242466 +L 237 76314 +L 190 30590 +G 159 1 +L 889 40894 +G 2401 7 +L 486 78246 +10 +L 719 612588 +G 126 6 +L 642 91164 +L 377 321204 +G 4828 142 +L 957 271788 +G 781 71 +L 869 740388 +L 897 254748 +L 6660 472860 +1 +G 4 2 +1 +L 4 2 +3 +G 18 6 +L 5 60 +G 20 4 +2 +G 18 6 +G 36 9 +3 +L 123 123 +L 234 234 +L 345 345 +12 +G 2 2 +G 3 3 +G 5 5 +G 7 7 +G 11 11 +G 13 13 +G 17 17 +G 19 19 +G 23 23 +G 29 29 +G 31 31 +G 37 37 +10 +G 2 2 +G 3 3 +G 5 5 +G 7 7 +G 11 11 +G 13 13 +G 17 17 +G 19 19 +G 23 23 +G 29 29 +9 +G 2 2 +G 3 3 +G 5 5 +G 7 7 +G 11 11 +G 13 13 +G 17 17 +G 19 19 +G 23 23 +2 +G 193939 199933 +G 199933 193939 +3 +L 2 1 +L 3 1 +L 5 10 +2 +G 1 199933 +G 1 193939 +1 +G 32 25 +1 +L 25 32 +3 +G 81 81 +G 37 37 +G 333667 333667 +2 +G 512 512 +G 1953125 1953125 +5 +G 7 7 +G 11 11 +G 13 13 +G 19 19 +G 52579 52579 +1 +L 300000007 600000000 +2 +L 85 50235 +G 886 2 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34932 diff --git a/2019/round3/integers_as_service.md b/2019/round3/integers_as_service.md new file mode 100644 index 0000000000000000000000000000000000000000..af0ad6c9c15ba7826ed278c04d8d6775ef65a315 --- /dev/null +++ b/2019/round3/integers_as_service.md @@ -0,0 +1,63 @@ +Looking for a new direction for his company, Carlos wants to break into the +most exciting tech field: digital rights management (DRM). In the world of +DRM, mega-corporations wage perpetual war against a vast sea of e-pirates, +modern-day Robin Hoods of ambiguous moral character. + +One of the biggest players in this struggle is Sony, the well-known +copyrighter of numbers. Considering the speed with which Sony puts out new +products, it's no wonder they're having trouble coming up with enough secret +encryption keys to protect all of their intellectual property. Enter Carlos. + +_ "Gone are the days of paying over-priced number theory PhDs to craft primes +by hand. I can make you a system that will generate all the numbers you need, +to your exact specifications." _ + +Sony wants to see a demonstration of Carlos's system before forking over +millions of dollars in consultancy fees. They have some new products in +development, each of which requires a secret key, **X**. For each key, Sony +has a list of **N** requirements. The _i_th requirement has an operator +character **Oi**, an integer value **Vi**, and an integer result **Ri**. + +When **Oi** is 'G', the _i_th requirement states that the greatest common +divisor of **X** and **Vi** must be **Ri**. That is, `GCD(X, Vi) = Ri`. + +When **Oi** is 'L', the _i_th requirement states that the least common +multiple of **X** and **Vi** must be **Ri**. That is, `LCM(X, Vi) = Ri`. + +There is also a global requirement that all of Sony's secret keys must be +positive integers no larger than 1,000,000,000. Help Carlos build any positive +integer **X** consistent with all of these requirements, or determine that no +such integer exists. + +### Input + +Input begins with an integer **T**, the number of secret keys that Sony wants +Carlos to generate. For each number, there is first a line containing the +integer **N**. Then, **N** lines follow, the _i_th of which contains the +character **Oi**, and the integers **Vi** and **Ri**, all separated by spaces. + +### Output + +For the _i_th secret key, print a line containing "Case #_i_: " followed by a +single integer: your chosen value of **X**, or -1 if no valid integer **X** +exists. + +### Constraints + +1 ≤ **T** ≤ 250 +1 ≤ **N** ≤ 2,000 +**Oi** ∈ {'G', 'L'} +1 ≤ **Vi**, **Ri** ≤ 1,000,000,000 + +### Explanation of Sample + +In the first case, `GCD(6, 4) = 2`, meaning that **X** = 6 satisfies the one +and only requirement. Note that, for this case and potentially other cases +below, **various other outputs will also be accepted**. + +In the second case, there exists no valid integer **X** such that 1 ≤ **X** ≤ +1,000,000,000 and `LCM(X, 4) = 2`. + +In the third case, `GCD(24, 18) = 6`, `LCM(24, 40) = 120`, and `GCD(24, 20) = +4`, meaning that **X** = 24 is a valid choice. + diff --git a/2019/round3/integers_as_service.out b/2019/round3/integers_as_service.out new file mode 100644 index 0000000000000000000000000000000000000000..440876e8d5852cd86d34549b8c6328405bef7649 --- /dev/null +++ b/2019/round3/integers_as_service.out @@ -0,0 +1,542 @@ +Case #1: 2 +Case #2: -1 +Case #3: 12 +Case #4: -1 +Case #5: 424179 +Case #6: -1 +Case #7: 1000000000 +Case #8: -1 +Case #9: 33920 +Case #10: -1 +Case #11: 322 +Case #12: -1 +Case #13: 2 +Case #14: -1 +Case #15: 12 +Case #16: -1 +Case #17: 1 +Case #18: -1 +Case #19: -1 +Case #20: 223092870 +Case #21: -1 +Case #22: -1 +Case #23: -1 +Case #24: -1 +Case #25: -1 +Case #26: 999999999 +Case #27: 1000000000 +Case #28: -1 +Case #29: -1 +Case #30: -1 +Case #31: 123456791 +Case #32: 123456791 +Case #33: 1 +Case #34: 1 +Case #35: 456789143 +Case #36: -1 +Case #37: -1 +Case #38: -1 +Case #39: -1 +Case #40: 119 +Case #41: 531 +Case #42: -1 +Case #43: 7 +Case #44: -1 +Case #45: -1 +Case #46: -1 +Case #47: 12 +Case #48: 481 +Case #49: 387 +Case #50: 403 +Case #51: 26 +Case #52: 575 +Case #53: 672 +Case #54: -1 +Case #55: 32 +Case #56: 119 +Case #57: 531 +Case #58: 18328 +Case #59: -1 +Case #60: 2 +Case #61: 2001 +Case #62: -1 +Case #63: 389 +Case #64: 88 +Case #65: -1 +Case #66: 1 +Case #67: 89 +Case #68: 594 +Case #69: 802 +Case #70: 3 +Case #71: -1 +Case #72: -1 +Case #73: -1 +Case #74: 199 +Case #75: 555 +Case #76: 1 +Case #77: 577 +Case #78: 244 +Case #79: 1 +Case #80: 839 +Case #81: 751 +Case #82: 118 +Case #83: 225 +Case #84: 914 +Case #85: 2 +Case #86: -1 +Case #87: 790 +Case #88: 13 +Case #89: -1 +Case #90: -1 +Case #91: 1 +Case #92: -1 +Case #93: 912 +Case 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#289: 1 +Case #290: 267 +Case #291: 294 +Case #292: 4 +Case #293: -1 +Case #294: 330 +Case #295: 77 +Case #296: 198 +Case #297: 279 +Case #298: -1 +Case #299: 640 +Case #300: 413 +Case #301: 7 +Case #302: 984 +Case #303: 794 +Case #304: 10 +Case #305: -1 +Case #306: 371 +Case #307: 33 +Case #308: 465 +Case #309: 431 +Case #310: 1 +Case #311: 656 +Case #312: 496 +Case #313: 16 +Case #314: 362 +Case #315: 762 +Case #316: 3 +Case #317: -1 +Case #318: 791 +Case #319: -1 +Case #320: 192 +Case #321: 778 +Case #322: -1 +Case #323: 490 +Case #324: 479 +Case #325: 224 +Case #326: -1 +Case #327: 242 +Case #328: 3 +Case #329: 323 +Case #330: 844 +Case #331: 685 +Case #332: -1 +Case #333: -1 +Case #334: 14 +Case #335: -1 +Case #336: 216 +Case #337: 7245 +Case #338: 1 +Case #339: 446 +Case #340: 2 +Case #341: -1 +Case #342: 915 +Case #343: 239 +Case #344: 989 +Case #345: -1 +Case #346: -1 +Case #347: -1 +Case #348: 612 +Case #349: 1 +Case #350: 405 +Case #351: 671 +Case #352: 13 +Case #353: 457 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+Case #484: 2 +Case #485: 891 +Case #486: 690 +Case #487: 5 +Case #488: 563 +Case #489: 716 +Case #490: 1 +Case #491: 435 +Case #492: 112 +Case #493: 1 +Case #494: 857 +Case #495: -1 +Case #496: 67 +Case #497: 361 +Case #498: 777 +Case #499: 6 +Case #500: 327 +Case #501: -1 +Case #502: -1 +Case #503: 310 +Case #504: 602 +Case #505: 1 +Case #506: 757 +Case #507: -1 +Case #508: 1 +Case #509: 617 +Case #510: -1 +Case #511: 7 +Case #512: 103 +Case #513: -1 +Case #514: 1 +Case #515: 841 +Case #516: 88 +Case #517: 1 +Case #518: 473 +Case #519: 263 +Case #520: 413 +Case #521: 49 +Case #522: 441 +Case #523: 1 +Case #524: 966 +Case #525: 562 +Case #526: 247 +Case #527: 244 +Case #528: 522 +Case #529: 4 +Case #530: 139 +Case #531: 211 +Case #532: 1 +Case #533: 445 +Case #534: 938 +Case #535: 3 +Case #536: 852 +Case #537: 60 +Case #538: 1 +Case #539: 463 +Case #540: 568 +Case #541: 4 +Case #542: 164 diff --git a/2019/round3/light_show.cpp b/2019/round3/light_show.cpp new file mode 100644 index 0000000000000000000000000000000000000000..5c1394cbfb6af883c1f24cfca114422a2532953b --- /dev/null +++ b/2019/round3/light_show.cpp @@ -0,0 +1,133 @@ +// Light Show +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +#define LIM 4001 + +int main() +{ + if (DEBUG) + freopen("in.txt","r",stdin); + // vars + int T,t; + int H,N; + int i,j,c,d; + PR P[LIM]; + static int dyn[LIM][LIM][2]; + // testcase loop + Read(T); + Fox1(t,T) + { + // input + Read(H),Read(N); + Fox(i,N) + Read(P[i].x),Read(P[i].y),P[i].y--; + // sort by position + sort(P,P+N); + // DP + Fill(dyn,-1); + dyn[0][0][0]=0; + Fox(i,N) + Fox(j,i+1) + Fox(c,2) + if ((d=dyn[i][j][c])>=0) + if (P[i].y==c) + Max(dyn[i+1][j+1][c],d+j); // add on + else + { + Max(dyn[i+1][j][c],d); // skip + Max(dyn[i+1][1][1-c],d); // switch colour + } + // find answer + int ans=0; + Fox(j,N+1) + Fox(c,2) + Max(ans,dyn[N][j][c]); + // output + printf("Case #%d: %d\n",t,ans); + } + return(0); +} \ No newline at end of file diff --git a/2019/round3/light_show.html b/2019/round3/light_show.html new file mode 100644 index 0000000000000000000000000000000000000000..13158fe13570ebd5bfe417a1ef2311d3ca993313 --- /dev/null +++ b/2019/round3/light_show.html @@ -0,0 +1,85 @@ +

+Melody is visiting the renowned Notre-Dame Basilica church in Montréal, Canada. +Aside from appreciating its beautiful architecture, she's there to see a spectacular light show scheduled to be held within! +

+ +

+Representing the cross-sectional view of the church as a 2D plane, it has a mirror-covered ceiling made up of two 45-degree line segments, +the first running from (0, 0) to (H, H) and the second running from (H, H) to (2H, 0). +

+ +

+N lasers have been set up on the floor, pointing upwards, with the ith one at integral coordinates (Xi, 0) +emitting a coloured beam of either red (if Ci = 1) or blue (if Ci = 2) light. +All N lasers are at distinct positions, and there's no laser directly under the center of the ceiling (at x-coordinate H). +If uninterrupted, each laser's beam travels vertically upwards until it hits a point on the ceiling, at which point it bounces to travel horizontally until it hits another point on the ceiling, at which point it bounces to travel vertically downwards and eventually hits another point on the floor. No laser has been set up such that its beam can possibly end up directly hitting another laser at the end of its path. In other words, if there's a laser at coordinates (x, 0), there's guaranteed to be no laser at coordinates (2H - x, 0). +

+ +

+For example, if H = 5 and there's a single red laser at coordinates (7, 0), the church would look as follows: +

+ + + +

+Melody thinks it looks pretty when laser beams interact with one another, but not when red and blue beams clash, so she's going to take matters into her own hands to optimize the show's appearance. She will use drones to suspend 0 or more blockers in the air within the church, each occupying a single point (possibly with non-integral coordinates) strictly above the x-axis and strictly underneath the ceiling. Each laser beam stops traveling as soon as it hits a blocker. +

+ +

+Let I(i, j) be true if lasers i and j intersect (in other words, if there exists at least one point which both of their beams pass through). +If two laser beams hit the same blocker, they are not considered to intersect at that blocker's coordinates. The quality Q of a light show, in Melody's eyes, is the number of +unordered pairs of laser beams (i, j) for which I(i, j) is true and Ci = Cj. +However, if there is any intersecting pair of differently-coloured laser beams (i.e. there exists some pair of beams (i, j) for which I(i, j) is true and CiCj), +then the quality of the light show is instead 0. +

+ + +

Input

+ +

+Input begins with an integer T, the number of light shows that Melody watches. +For each show, there is first a line containing the space-separated integers H and N. +Then, N lines follow, the ith of which contains the space-separated integers Xi and Ci. +

+ + +

Output

+ +

+For the ith show, print a line containing "Case #i: " +followed by a single integer Q, the maximum possible quality of the light show. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 150
+2 ≤ H ≤ 1,000,000,000
+1 ≤ N ≤ 4,000
+1 ≤ Xi ≤ 2H - 1
+XiH
+1 ≤ Ci ≤ 2
+

+ +

Explanation of Sample

+ +

+In the first case, if no blockers are placed, all three unordered pairs of red lasers will intersect with one another for a quality of 3: +

+ + + +

+In the second case, if Melody were to place no blockers, there would be two same-colour laser beam intersections (one involving the red lasers and another involving the blue ones), +but there would also be at least one different-colour laser beam intersection, so this is not ideal as the quality is 0: +

+ + + +

+If she instead places one blocker at coordinates (2.5, 1), blocking the first laser, and another at (6, 2), blocking both both the second and fourth lasers, +then one same-colour laser beam intersection would be achieved (between the second and third lasers at coordinates (7, 2)) for a quality of 1: +

+ + diff --git a/2019/round3/light_show.in b/2019/round3/light_show.in new file mode 100644 index 0000000000000000000000000000000000000000..9b373739a2add0b117d51365c4f0c494e2580fb7 --- /dev/null +++ b/2019/round3/light_show.in @@ -0,0 +1,260172 @@ +513 +5 3 +4 1 +9 1 +2 1 +5 4 +1 1 +8 2 +3 2 +6 1 +12 6 +15 2 +22 1 +4 2 +14 1 +23 1 +19 2 +53 9 +7 1 +19 1 +23 2 +40 2 +54 2 +81 1 +85 2 +94 1 +102 1 +8128376 30 +259694 2 +10267200 2 +591548 2 +5755696 2 +4307513 2 +5863522 2 +10040589 1 +2234412 1 +5086932 1 +14706276 1 +15430629 2 +2150128 2 +14561793 1 +7991506 2 +824138 2 +3450600 2 +6482303 1 +11413148 1 +12215231 2 +7578498 1 +13184008 2 +6684996 1 +11579040 1 +2662824 1 +13334004 2 +5954542 1 +7364389 1 +8028062 1 +11858536 1 +15223536 2 +2 1 +1 1 +2 1 +3 1 +3 2 +1 1 +2 2 +3 2 +1 1 +2 1 +3 2 +1 1 +4 1 +3 2 +1 1 +4 2 +100 20 +1 1 +2 1 +3 2 +4 2 +5 2 +6 2 +7 2 +8 2 +9 2 +10 2 +11 1 +12 1 +13 1 +14 1 +15 1 +16 1 +17 1 +18 1 +19 2 +20 2 +1000000000 464 +1 1 +199999999 2 +2 1 +199999998 2 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--git a/2019/round3/light_show.md b/2019/round3/light_show.md new file mode 100644 index 0000000000000000000000000000000000000000..2cc5289ba77067920c726ee9bedac9f4580ee170 --- /dev/null +++ b/2019/round3/light_show.md @@ -0,0 +1,76 @@ +Melody is visiting the renowned Notre-Dame Basilica church in Montréal, +Canada. Aside from appreciating its beautiful architecture, she's there to see +a spectacular light show scheduled to be held within! + +Representing the cross-sectional view of the church as a 2D plane, it has a +mirror-covered ceiling made up of two 45-degree line segments, the first +running from (0, 0) to (**H**, **H**) and the second running from (**H**, +**H**) to (2**H**, 0). + +**N** lasers have been set up on the floor, pointing upwards, with the _i_th one at integral coordinates (**Xi**, 0) emitting a coloured beam of either red (if **Ci** = 1) or blue (if **Ci** = 2) light. All **N** lasers are at distinct positions, and there's no laser directly under the center of the ceiling (at x-coordinate **H**). If uninterrupted, each laser's beam travels vertically upwards until it hits a point on the ceiling, at which point it bounces to travel horizontally until it hits another point on the ceiling, at which point it bounces to travel vertically downwards and eventually hits another point on the floor. No laser has been set up such that its beam can possibly end up directly hitting another laser at the end of its path. In other words, if there's a laser at coordinates (x, 0), there's guaranteed to be no laser at coordinates (2**H** \- x, 0). + +For example, if **H** = 5 and there's a single red laser at coordinates (7, +0), the church would look as follows: + +![]({{PHOTO_ID:984673281988054}}) + +Melody thinks it looks pretty when laser beams interact with one another, but +not when red and blue beams clash, so she's going to take matters into her own +hands to optimize the show's appearance. She will use drones to suspend 0 or +more blockers in the air within the church, each occupying a single point +(possibly with non-integral coordinates) strictly above the x-axis and +strictly underneath the ceiling. Each laser beam stops traveling as soon as it +hits a blocker. + +Let `I(i, j)` be true if lasers _i_ and _j_ intersect (in other words, if +there exists at least one point which both of their beams pass through). If +two laser beams hit the same blocker, they are not considered to intersect at +that blocker's coordinates. The quality **Q** of a light show, in Melody's +eyes, is the number of unordered pairs of laser beams (_i_, _j_) for which +`I(i, j)` is true and **Ci** = **Cj**. However, if there is any intersecting +pair of differently-coloured laser beams (i.e. there exists some pair of beams +(_i_, _j_) for which `I(i, j)` is true and **Ci** ≠ **Cj**), then the quality +of the light show is instead 0. + +### Input + +Input begins with an integer **T**, the number of light shows that Melody +watches. For each show, there is first a line containing the space-separated +integers **H** and **N**. Then, **N** lines follow, the _i_th of which +contains the space-separated integers **Xi** and **Ci**. + +### Output + +For the _i_th show, print a line containing "Case #_i_: " followed by a single +integer **Q**, the maximum possible quality of the light show. + +### Constraints + +1 ≤ **T** ≤ 150 +2 ≤ **H** ≤ 1,000,000,000 +1 ≤ **N** ≤ 4,000 +1 ≤ **Xi** ≤ 2**H** \- 1 +**Xi** ≠ **H** +1 ≤ **Ci** ≤ 2 + +### Explanation of Sample + +In the first case, if no blockers are placed, all three unordered pairs of red +lasers will intersect with one another for a quality of 3: + +![]({{PHOTO_ID:945646162539269}}) + +In the second case, if Melody were to place no blockers, there would be two +same-colour laser beam intersections (one involving the red lasers and another +involving the blue ones), but there would also be at least one different- +colour laser beam intersection, so this is not ideal as the quality is 0: + +![]({{PHOTO_ID:282212846231841}}) + +If she instead places one blocker at coordinates (2.5, 1), blocking the first +laser, and another at (6, 2), blocking both both the second and fourth lasers, +then one same-colour laser beam intersection would be achieved (between the +second and third lasers at coordinates (7, 2)) for a quality of 1: + +![]({{PHOTO_ID:711991349348175}}) + diff --git a/2019/round3/light_show.out b/2019/round3/light_show.out new file mode 100644 index 0000000000000000000000000000000000000000..b650dfea61372942f762f37765375266110815ae --- /dev/null +++ b/2019/round3/light_show.out @@ -0,0 +1,513 @@ +Case #1: 3 +Case #2: 1 +Case #3: 4 +Case #4: 10 +Case #5: 112 +Case #6: 0 +Case #7: 0 +Case #8: 0 +Case #9: 1 +Case #10: 1 +Case #11: 0 +Case #12: 58 +Case #13: 40672 +Case #14: 1999000 +Case #15: 7986006 +Case #16: 1989021 +Case #17: 2096131 +Case #18: 2089993 +Case #19: 2027091 +Case #20: 1957241 +Case #21: 2077741 +Case #22: 1977069 +Case #23: 2143485 +Case #24: 2025078 +Case #25: 2007006 +Case #26: 1951300 +Case #27: 2009011 +Case #28: 2087946 +Case #29: 1945378 +Case #30: 1935528 +Case #31: 1888596 +Case #32: 2013022 +Case #33: 1925714 +Case #34: 1999001 +Case #35: 7502001 +Case #36: 2049301 +Case #37: 1957231 +Case #38: 2114596 +Case #39: 2007007 +Case #40: 2007006 +Case #41: 1981046 +Case #42: 2031120 +Case #43: 1756875 +Case #44: 1817374 +Case #45: 2627778 +Case #46: 1813560 +Case #47: 1869212 +Case #48: 2061465 +Case #49: 1815466 +Case #50: 1898332 +Case #51: 1991011 +Case #52: 1830741 +Case #53: 1925709 +Case #54: 1880831 +Case #55: 7673403 +Case #56: 1684530 +Case #57: 1727011 +Case #58: 1717732 +Case #59: 1925709 +Case #60: 1736322 +Case #61: 1788888 +Case #62: 1863415 +Case #63: 1819293 +Case #64: 561 +Case #65: 4097 +Case #66: 1081 +Case #67: 633 +Case #68: 300 +Case #69: 9870 +Case #70: 3 +Case #71: 601 +Case #72: 153 +Case #73: 354 +Case #74: 3 +Case #75: 81 +Case #76: 1541 +Case #77: 1540 +Case #78: 2212 +Case #79: 11476 +Case #80: 6 +Case #81: 2926 +Case #82: 3081 +Case #83: 2926 +Case #84: 8778 +Case 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11325 +Case #444: 409 +Case #445: 903 +Case #446: 79 +Case #447: 6 +Case #448: 154 +Case #449: 561 +Case #450: 137 +Case #451: 2629 +Case #452: 1540 +Case #453: 2415 +Case #454: 1228 +Case #455: 13 +Case #456: 8661 +Case #457: 0 +Case #458: 11794 +Case #459: 5892 +Case #460: 435 +Case #461: 10022 +Case #462: 669 +Case #463: 4466 +Case #464: 633 +Case #465: 946 +Case #466: 120 +Case #467: 9046 +Case #468: 6788 +Case #469: 990 +Case #470: 0 +Case #471: 139 +Case #472: 6670 +Case #473: 5360 +Case #474: 2211 +Case #475: 10443 +Case #476: 630 +Case #477: 1653 +Case #478: 4851 +Case #479: 4754 +Case #480: 2415 +Case #481: 1834 +Case #482: 12410 +Case #483: 1128 +Case #484: 11026 +Case #485: 10440 +Case #486: 306 +Case #487: 384 +Case #488: 1 +Case #489: 4465 +Case #490: 211 +Case #491: 13041 +Case #492: 9591 +Case #493: 1128 +Case #494: 5889 +Case #495: 8414 +Case #496: 9316 +Case #497: 7141 +Case #498: 3403 +Case #499: 353 +Case #500: 5784 +Case #501: 7260 +Case #502: 5151 +Case #503: 48 +Case #504: 1712 +Case #505: 5151 +Case #506: 10731 +Case #507: 436 +Case #508: 9871 +Case #509: 5154 +Case #510: 8646 +Case #511: 5151 +Case #512: 4657 +Case #513: 3003 diff --git a/2019/round3/renovations.cpp b/2019/round3/renovations.cpp new file mode 100644 index 0000000000000000000000000000000000000000..9c02cb34eb40373ff5913b037f7334afc3386b28 --- /dev/null +++ b/2019/round3/renovations.cpp @@ -0,0 +1,207 @@ +// Renovations +// Solution by Jacob Plachta + +#define DEBUG 0 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; + +#define LL long long +#define LD long double +#define PR pair + +#define Fox(i,n) for (i=0; i=0; i--) +#define FoxR1(i,n) for (i=n; i>0; i--) +#define FoxRI(i,a,b) for (i=b; i>=a; i--) +#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) +#define Min(a,b) a=min(a,b) +#define Max(a,b) a=max(a,b) +#define Sz(s) int((s).size()) +#define All(s) (s).begin(),(s).end() +#define Fill(s,v) memset(s,v,sizeof(s)) +#define pb push_back +#define mp make_pair +#define x first +#define y second + +template T Abs(T x) { return(x<0 ? -x : x); } +template T Sqr(T x) { return(x*x); } +string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); } + +const int INF = (int)1e9; +const LD EPS = 1e-12; +const LD PI = acos(-1.0); + +#if DEBUG +#define GETCHAR getchar +#else +#define GETCHAR getchar_unlocked +#endif + +bool Read(int &x) +{ + char c,r=0,n=0; + x=0; + for(;;) + { + c=GETCHAR(); + if ((c<0) && (!r)) + return(0); + if ((c=='-') && (!r)) + n=1; + else + if ((c>='0') && (c<='9')) + x=x*10+c-'0',r=1; + else + if (r) + break; + } + if (n) + x=-x; + return(1); +} + +#define LIM 6001 +#define MOD 1000000007 + +int N,K; +int expMem[LIM]; + +int Exp(int a,int b) +{ + if ((a>=1; + } + if ((a qA,qB; + for (dA=0; A>=0; A=P[A],dA++) + qA.push(A); + for (dB=0; B>=0; B=P[B],dB++) + qB.push(B); + dL=max(dA,dB); + for(;;) + { + if (qA.front()==qB.front()) + break; + dL--; + if (Sz(qA)>dL) + qA.pop(); + if (Sz(qB)>dL) + qB.pop(); + } + dL--,dA--,dB--; + // consider all possible final states + int ans=0; + if (!dL) // original LCA is the root? + { + Fox(A,dA+1) + Fox(B,dB+1) + { + if ((dA) && (!A) || (dB) && (!B)) + continue; + Add(ans,Prod(A+B,Count(A+B-(A?1:0)-(B?1:0),(AdA-dL) && (B>dB-dL)) + continue; + Add(ans,Prod(A+B,Count(A+B-2,(A +A family of four moles lives in an underground burrow. Each of them has an important role to play! Daddy Mole is in charge of renovating the burrow. +Mommy Mole fixes up Daddy Mole's inevitable mistakes. And Brother Mole and Sister Mole mostly lie around playing video games. +

+ +

+Their burrow consists of N little underground rooms, numbered from 1 to N. Room 1 is connected to the surface, +and for each other room i (such that 2 ≤ iN), the room initially "above" room i is room Pi, +meaning that there's a tunnel leading downwards from room Pi to room i, which may be traversed in either direction. +It's guaranteed that it's possible to reach each room from room 1 by travelling through a sequence of tunnels. +

+ +

+Daddy Mole will renovate the burrow K times in a row. For each renovation in turn, he'll independently randomly select a room i aside from room 1 +(such that 2 ≤ iN), with each such room having an equal 1 / (N - 1) probability of being chosen each time. +He'll then "improve" the burrow's architectural design by simply caving in the tunnel connecting node i and the room currently above it, causing that tunnel to no longer exist. +Mommy Mole will then immediately salvage the situation by creating a new tunnel leading downwards from room 1 to room i +(such that the room above i will now be room 1). +This may result in Mommy Mole recreating exactly the same tunnel that Daddy Mole had just caved in. Note that, in the resulting burrow, each room will always once again be reachable from room 1. +

+ +

+After these K random renovations have been completed, Brother Mole (who hangs out in room A) +will go visit Sister Mole in her room (room B) to show off his latest video game high score. +He'll travel along the unique sequence of tunnels which will get him there without passing through any rooms multiple times, at a speed of 1 tunnel per minute. +What's the expected amount of time this will take him? +

+ +

+Let this expected time (in minutes) be represented as a quotient of integers p/q in lowest terms. +Output the value of this quotient modulo 1,000,000,007 — in other words, output the unique integer x such that +0 ≤ x < 1,000,000,007 and p = x*q (modulo 1,000,000,007). +

+ +

Input

+ +

+Input begins with an integer T, the number of burrows. +For each burrow, there is first a line containing the space-separated integers N, K, A, and B. +Then, N - 1 lines follow, the ith of which contains the integer Pi+1 (starting with P2). +

+ + +

Output

+ +

+For the ith burrow, print a line containing "Case #i: " followed by a single integer, the expected number of minutes required for Brother Mole +to travel from room A to room B after K renovations, expressed as a quotient of integers modulo 1,000,000,007. +

+ + +

Constraints

+ +

+1 ≤ T ≤ 70
+2 ≤ N ≤ 6,000
+0 ≤ K ≤ 2,000,000
+1 ≤ A, B, PiN
+AB
+

+ + +

Explanation of Sample

+ +

+In the first case, if Daddy Mole chooses room 2 for his single renovation (caving in the tunnel between rooms 2 and 3), then Mommy Mole will dig a tunnel between rooms 1 and 2, +and Brother Mole will then need 2 minutes to travel from room 2 to room 3 (passing through room 1 along the way). Otherwise, if Daddy Mole chooses node 3, +then Mommy Mole will restore the burrow to its original state, and Brother Mole will be able to reach room 3 directly in 1 minute. +These two possibilities are equally likely, resulting in an expected time of (2+1)/2 = 3/2 = 500000005 (modulo 1,000,000,007) minutes. +

+ +

+In the second case, no matter which room Daddy Mole chooses for each renovation, Mommy Mole will recreate the tunnel that he caves in, +resulting in Brother Mole's trip taking 2 minutes after any number of renovations. +

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+23 +22 +31 +55 +8 +59 +2 +43 +37 +28 +15 +35 +45 +54 +51 +38 +44 +7 +22 +33 +54 +3 +39 +1 +48 +14 +34 +30 +32 +1 +11 +10 +27 +43 +24 +40 diff --git a/2019/round3/renovations.md b/2019/round3/renovations.md new file mode 100644 index 0000000000000000000000000000000000000000..6ee39f260a60faa94070d13ef19a4181d2e94ad4 --- /dev/null +++ b/2019/round3/renovations.md @@ -0,0 +1,73 @@ +A family of four moles lives in an underground burrow. Each of them has an +important role to play! Daddy Mole is in charge of renovating the burrow. +Mommy Mole fixes up Daddy Mole's inevitable mistakes. And Brother Mole and +Sister Mole mostly lie around playing video games. + +Their burrow consists of **N** little underground rooms, numbered from 1 to +**N**. Room 1 is connected to the surface, and for each other room _i_ (such +that 2 ≤ _i_ ≤ **N**), the room initially "above" room _i_ is room **Pi**, +meaning that there's a tunnel leading downwards from room **Pi** to room _i_, +which may be traversed in either direction. It's guaranteed that it's possible +to reach each room from room 1 by travelling through a sequence of tunnels. + +Daddy Mole will renovate the burrow **K** times in a row. For each renovation +in turn, he'll independently randomly select a room _i_ aside from room 1 +(such that 2 ≤ _i_ ≤ **N**), with each such room having an equal 1 / (**N** \- +1) probability of being chosen each time. He'll then "improve" the burrow's +architectural design by simply caving in the tunnel connecting node _i_ and +the room currently above it, causing that tunnel to no longer exist. Mommy +Mole will then immediately salvage the situation by creating a new tunnel +leading downwards from room 1 to room _i_ (such that the room above _i_ will +now be room 1). This may result in Mommy Mole recreating exactly the same +tunnel that Daddy Mole had just caved in. Note that, in the resulting burrow, +each room will always once again be reachable from room 1. + +After these **K** random renovations have been completed, Brother Mole (who +hangs out in room **A**) will go visit Sister Mole in her room (room **B**) to +show off his latest video game high score. He'll travel along the unique +sequence of tunnels which will get him there without passing through any rooms +multiple times, at a speed of 1 tunnel per minute. What's the expected amount +of time this will take him? + +Let this expected time (in minutes) be represented as a quotient of integers +**p/q** in lowest terms. Output the value of this quotient modulo +1,000,000,007 — in other words, output the unique integer **x** such that 0 ≤ +**x** < 1,000,000,007 and **p** = **x*****q** (modulo 1,000,000,007). + +### Input + +Input begins with an integer **T**, the number of burrows. For each burrow, +there is first a line containing the space-separated integers **N**, **K**, +**A**, and **B**. Then, **N** \- 1 lines follow, the _i_th of which contains +the integer **Pi+1** (starting with **P2**). + +### Output + +For the _i_th burrow, print a line containing "Case #_i_: " followed by a +single integer, the expected number of minutes required for Brother Mole to +travel from room **A** to room **B** after **K** renovations, expressed as a +quotient of integers modulo 1,000,000,007. + +### Constraints + +1 ≤ **T** ≤ 70 +2 ≤ **N** ≤ 6,000 +0 ≤ **K** ≤ 2,000,000 +1 ≤ **A**, **B**, **Pi** ≤ **N** +**A** ≠ **B** + +### Explanation of Sample + +In the first case, if Daddy Mole chooses room 2 for his single renovation +(caving in the tunnel between rooms 2 and 3), then Mommy Mole will dig a +tunnel between rooms 1 and 2, and Brother Mole will then need 2 minutes to +travel from room 2 to room 3 (passing through room 1 along the way). +Otherwise, if Daddy Mole chooses node 3, then Mommy Mole will restore the +burrow to its original state, and Brother Mole will be able to reach room 3 +directly in 1 minute. These two possibilities are equally likely, resulting in +an expected time of (2+1)/2 = 3/2 = 500000005 (modulo 1,000,000,007) minutes. + +In the second case, no matter which room Daddy Mole chooses for each +renovation, Mommy Mole will recreate the tunnel that he caves in, resulting in +Brother Mole's trip taking 2 minutes after any number of renovations. + diff --git a/2019/round3/renovations.out b/2019/round3/renovations.out new file mode 100644 index 0000000000000000000000000000000000000000..aa8617d33ba04971c1b9cdc84e52d7a54cdd8aad --- /dev/null +++ b/2019/round3/renovations.out @@ -0,0 +1,507 @@ +Case #1: 500000005 +Case #2: 2 +Case #3: 3 +Case #4: 480000006 +Case #5: 744000007 +Case #6: 344000005 +Case #7: 575944518 +Case #8: 925841127 +Case #9: 256354701 +Case #10: 542873565 +Case #11: 690669945 +Case #12: 253885328 +Case #13: 449851090 +Case #14: 43239667 +Case #15: 355115214 +Case #16: 837285316 +Case #17: 118417126 +Case #18: 397931947 +Case #19: 466633521 +Case #20: 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