#include #include using namespace std; const int INF = (int)1e9; struct fenwick { // For 1-based indices. vector a, t; fenwick(int N) : a(N + 1), t(N + 1) {} int sum(int hi) const { int res = 0; for (; hi > 0; hi -= hi & -hi) { res += t[hi]; } return res; } void inc(int i, int x) { a[i] += x; for (; i < (int)t.size(); i += i & -i) { t[i] += x; } } int at(int i) const { return a[i]; } int sum(int lo, int hi) const { return sum(hi) - sum(lo - 1); } void set(int i, int x) { inc(i, x - a[i]); } }; // Let L be the subarray with lower sum, and H be the one with higher sum. // Try to reduce d = sum(H) - sum(L) down to 0 with the follow operations: // 1. Decrease d by 4 by swapping a 1 in L with a 3 in H. // 2. Decrease d by 2 by swapping a 1 in L with a 2 in H, // or a 2 in L with a 3 in H. // 3. Increase d by 2 by swapping a 2 in L with a 1 in H, // or a 3 in L with a 2 in H. // Update L/H after swapping v1 in L with v2 in H a total of swaps times. void do_swaps(vector &L, vector &H, int v1, int v2, int swaps) { L[v1] -= swaps; H[v1] += swaps; H[v2] -= swaps; L[v2] += swaps; } // Perform op 1 until no longer possible or d = 0 or 1. Then op 2 for the rest. int strategy_a(vector L, vector H, int d) { // We can perform op 1 at most min(num 1s in L, num 3s in H) times. // Each swap reduces d by 4, so we should also swap no more than floor(d/4). int swap13 = min(min(L[0], H[2]), d / 4); do_swaps(L, H, 0, 2, swap13); d -= 4*swap13; // Do the rest as needed with L[0], H[1] and L[1], H[2]. int swap12 = min(min(L[0], H[1]), d / 2); do_swaps(L, H, 0, 1, swap12); d -= 2*swap12; int swap23 = min(min(L[1], H[2]), d / 2); do_swaps(L, H, 1, 2, swap23); d -= 2*swap23; return d != 0 ? INF : swap13 + swap12 + swap23; } // Perform op 1 until d becomes equal to -1, then perform op 3 once. int strategy_b(vector L, vector H, int d) { // This time we can let d go below 0 by swapping up to ceil(d/4). int swap13 = min(min(L[0], H[2]), d / 4 + (int)(d % 4 != 0)); do_swaps(L, H, 0, 2, swap13); d -= 4*swap13; // Only if d < 0, try to bring d back up to 0 with more swaps. int swap21 = min(min(L[1], H[0]), d < 0 ? (-d)/2 : 0); do_swaps(L, H, 1, 0, swap21); d += 2*swap21; int swap32 = min(min(L[2], H[1]), d < 0 ? (-d)/2 : 0); do_swaps(L, H, 2, 1, swap32); d += 2*swap32; return d != 0 ? INF : swap13 + swap21 + swap32; } long long solve() { int N, M; cin >> N >> M; fenwick T[]{fenwick(N), fenwick(N), fenwick(N)}; for (int i = 1, a; i <= N; i++) { cin >> a; T[--a].set(i, 1); } long long ans = 0; for (int i = 0, x, y, z; i < M; i++) { cin >> x >> y >> z; --y; for (int v : {0, 1, 2}) { T[v].set(x, v == y); } vector L(3), H(3); int sumL = 0, sumH = 0; for (int v : {0, 1, 2}) { L[v] = T[v].sum(1, z); H[v] = T[v].sum(z + 1, N); sumL += (v + 1) * L[v]; sumH += (v + 1) * H[v]; } if (sumL == sumH) { continue; } if (sumL > sumH) { swap(sumL, sumH); L.swap(H); } int d = sumH - sumL; int swaps_a = strategy_a(L, H, d), swaps_b = strategy_b(L, H, d); int Q = min(swaps_a, swaps_b); ans += (Q == INF) ? -1 : Q; } 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; }