// This should be WA #include #include #include #include #include using namespace std; #include using mint = atcoder::modint1000000007; template int rank_of_matrix(std::vector> &M) { const int N = M.size(); int rank = 0; for (int i = 0; i < N; ++i) { int ti = i; while (ti < N and M[ti][i] == 0) ti++; if (ti == N) continue; ++rank; M[i].swap(M[ti]); T inv = T(1) / M[i][i]; for (int j = i + 1; j < N; ++j) M[i][j] *= inv; for (int h = 0; h < N; ++h) { if (i == h) continue; const T c = -M[h][i]; for (int j = i + 1; j < N; ++j) M[h][j] += M[i][j] * c; } } return rank; } mt19937 mt(1967176539); uniform_int_distribution rndgen(0, mint::mod()); int solve(int N, const vector> &uvws) { vector M(N, vector(N)); // Not bc - cb but bc + cb for (auto [u, v, w] : uvws) { int x = rndgen(mt); M[u][v] += x; M[v][u] += x; M[v][w] += x; M[w][v] += x; M[v][v] -= x; M[u][w] -= x; M[w][u] -= x; } return rank_of_matrix(M) / 2; } int main() { int N, M; cin >> N >> M; vector> uvws; while (M--) { int u, v, w; cin >> u >> v >> w; u--, v--, w--; uvws.emplace_back(u, v, w); } cout << solve(N, uvws) << '\n'; }