#include #include #include using namespace std; using LL = long long; struct fenwick { // For 1-based indices. vector a, t; fenwick(int N) : a(N + 1), t(N + 1) {} LL sum(int hi) const { LL res = 0; for (; hi > 0; hi -= hi & -hi) { res += t[hi]; } return res; } void inc(int i, LL x) { a[i] += x; for (; i < (int)t.size(); i += i & -i) { t[i] += x; } } LL at(int i) const { return a[i]; } LL sum(int lo, int hi) const { return sum(hi) - sum(lo - 1); } void set(int i, LL x) { inc(i, x - a[i]); } }; template int binary_search_last_true(int lo_incl, int hi_excl, Predicate pred) { int mid, lo = lo_incl, hi = hi_excl - 1; while (lo < hi) { mid = lo + (hi - lo + 1) / 2; if (pred(mid)) { lo = mid; } else { hi = mid - 1; } } return pred(lo) ? lo : hi_excl; } LL solve() { int N, M; cin >> N >> M; auto rev = [=](int i) -> int { return N - i + 1; }; fenwick Tv_fwd(N), Ti_fwd(N), Tv_rev(N), Ti_rev(N); for (int i = 1, a; i <= N; i++) { cin >> a; Tv_fwd.set(i, a == 2); Ti_fwd.set(i, a == 2 ? i : 0); Tv_rev.set(rev(i), a == 2); Ti_rev.set(rev(i), a == 2 ? i : 0); } LL ans = 0; for (int i = 0, x, y, z; i < M; i++) { cin >> x >> y >> z; Tv_fwd.set(x, y == 2); Ti_fwd.set(x, y == 2 ? x : 0); Tv_rev.set(rev(x), y == 2); Ti_rev.set(rev(x), y == 2 ? x : 0); int L2cnt = Tv_fwd.sum(1, z), H2cnt = Tv_fwd.sum(z + 1, N); int sumL = 1 * (z - L2cnt) + 2 * L2cnt; int sumH = 1 * (N - z - H2cnt) + 2 * H2cnt; if (sumL == sumH) { continue; } auto getQ = [&]( const fenwick &Tv, const fenwick &Ti, int d, int z, bool is_rev ) -> LL { int req2s = d / 2, tgt2s = Tv.sum(1, z) + req2s; if ( d % 2 == 1 || // Can't reduce d by an odd number with swaps. tgt2s > z || // Not enough room to fit all the 2's to make d = 0. req2s > Tv.sum(z + 1, N) // Not enough 2's from H to move over to L. ) { return -1; } // Assuming sumL < sumH, check that a choice of s will make sumL >= sumH // if we fill a A[s..z] by shifting 2's from A[(z+1)..N] leftwards, all // without touching the 2's in A[1..(s-1)]. int s = binary_search_last_true(1, z + 1, [&](int s) { // On the domain s=1..z, this predicate yields a pattern 1111000, as // we'll need force sufficiently many 2's in A[s..z] to hit the target // number of 2s required to make sumL = sumH. return Tv.sum(1, s - 1) + (z - s + 1) >= tgt2s; }); assert(s <= z); int c = z - s + 1; // Now compute the total cost of shifting the 2s from the range s..t // leftwards to fill the indices s..z. int t = 1 + binary_search_last_true(s, N + 1, [&](int t) { // On the domain t=s..N, this predicate yields a pattern 1111000, as // we'll need to choose sufficiently large t for there to be enough 2s. return Tv.sum(s, t) < c; }); assert(t <= N); // Q_i = (sum of final indices of 2s) - (sum of initial indices of 2s). if (is_rev) { return (LL)c*(rev(s) + rev(z))/2 - Ti.sum(s, t); } return Ti.sum(s, t) - (LL)c*(s + z)/2; }; if (sumL < sumH) { ans += getQ(Tv_fwd, Ti_fwd, sumH - sumL, z, false); } else { ans += getQ(Tv_rev, Ti_rev, sumL - sumH, rev(z) - 1, true); } } return ans; } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int T; cin >> T; for (int t = 1; t <= T; t++) { cout << "Case #" << t << ": " << solve() << endl; } return 0; }