| As the Jeremy Lin sensation goes on, Roger, who is a geek and a super fan of | |
| Jeremy Lin, decides his new cell phone number must be "Linsane". More | |
| specifically, he wants his new phone number to satisfy: | |
| 1) Adjacent sum: | |
| There is at least one occurrence in the phone number of three adjacent digits | |
| summing to **x**, where **x** is Lin's jersey number at New York Knicks. | |
| 2) Diversity: | |
| There are at least **y** different values of the digits used in the phone | |
| number, where **y** is Lin's jersey number at Golden State Warriors. | |
| 3) Neighboring difference: | |
| There is at least one pair of neighboring digits whose difference is equal to | |
| **z**, where **z** is Lin's jersey number at Harvard. | |
| A phone number with length **n** contains **n** digits. Each digit is in the | |
| range from 0 to 9, except that the first digit must be non-zero. | |
| A phone number is called "linsane" if it satisfies the three constraints | |
| listed above. | |
| For phone numbers with a given length **n**, Roger wonders how many "linsane" | |
| phone numbers exist. | |
| He also wants to find out the "most linsane" phone number among them. | |
| For a given length, the "most linsane" phone number is a "linsane" phone | |
| number that has the biggest "linsanity measurement" among them. | |
| "Linsanity measurement" is defined as , where **n** is the number of | |
| digits and **di** is the **i**-th digit in the phone number. | |
| If there is a tie on such measurement, choose the one whose median of the | |
| digits is largest; and if there is still a tie, choose the largest phone | |
| number. | |
| Median is the **(n+1)/2**-th smallest digit if **n** is odd, or the average of | |
| the **(n/2)**-th and **(n/2+1)**-th digit if **n** is even. For example, the | |
| linsanity measurement of number 78969251 is equal to (15*9)%8 + (17*6)%8 + | |
| (15*9)%8 + (15*2)%8 +(11*5)%8 + (7*1)%8 = 40 with its median equal to 6.5. | |
| ### Input | |
| The first line contains a positive integer **T**, the number of test cases. | |
| **T** test cases follow. | |
| Each test case is a single line and contains exactly four integers separated | |
| by single white space: **n x y z**, where **n** is the length of the phone | |
| number, **x** is Lin's jersey number at New York Knicks, **y** is Lin's jersey | |
| number at Golden State Warriors and **z** is Lin's jersey number at Harvard. | |
| (**x**,**y** and **z** are not necessarily 17, 7 and 4 in another parallel | |
| universe.) | |
| ### Constraints | |
| 3 ≤ **n** ≤ 20 | |
| 0 ≤ **x** ≤ 27 | |
| 0 ≤ **y** ≤ 10 | |
| 0 ≤ **z** ≤ 9 | |
| 1 ≤ **T** ≤ 15 | |
| Among the **T** test cases, there will be no more than 5 test cases with **n** | |
| >12. | |
| ### Output | |
| For each of the test cases numbered in order from **1** to **T**, output "Case | |
| #", followed by the case number, followed by ": ", followed by the number of | |
| possible "linsane" phone numbers _mod_ 1018 for the given length for that | |
| case, and then a single space " " followed by the "most linsane" phone number | |
| for the given length or -1 if no "linsane" phone number exists for the given | |
| length. | |