#include #include #include #include #include #include #include #include using namespace std; #include using mint = atcoder::static_modint<(1 << 30) + 3>; uint32_t rand_int() { static uint32_t x = 123456789, y = 362436069, z = 521288629, w = 88675123; uint32_t t = x ^ (x << 11); x = y; y = z; z = w; return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); } tuple>> read_input() { int N, M, X, Y, Z; cin >> N >> M >> X >> Y >> Z; --X, --Y, --Z; vector mat(N, vector(N)); for (int i = 0; i < N; ++i) { for (int j = 0; j < N; ++j) mat[i][j] = (i != j); } while (M--) { int a, b; cin >> a >> b; --a, --b; mat[a][b] = mat[b][a] = 0; } vector> to(N); for (int i = 0; i < N; ++i) { for (int j = 0; j < N; ++j) { if (mat[i][j]) to[i].push_back(j); } } return {N, X, Y, Z, to}; } template std::vector> inverse(std::vector> &tmp) { const int n = tmp.size(); std::vector> ret(n, std::vector(n)); for (int i = 0; i < n; ++i) ret[i][i] = 1; int rank = 0; for (int i = 0; i < n; ++i) { int ti = i; while (ti < n and tmp[ti][i] == 0) ++ti; if (ti == n) continue; ++rank; ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]); Fp inv = Fp(1) / tmp[i][i]; for (int j = 0; j < n; j++) ret[i][j] *= inv; for (int j = i + 1; j < n; j++) tmp[i][j] *= inv; for (int h = 0; h < n; h++) { if (i == h) continue; const Fp c = -tmp[h][i]; for (int j = 0; j < n; j++) ret[h][j] += ret[i][j] * c; for (int j = i + 1; j < n; j++) tmp[h][j] += tmp[i][j] * c; } } return ret; } template Fp determinant(std::vector> &M) { int n = M.size(); assert(int(M[0].size()) == n); Fp ret = 1; for (int i = 0; i < n; ++i) { int h = i; while (h < n and M[h][i] == 0) ++h; if (h == n) return 0; if (h != i) { M[h].swap(M[i]); ret = -ret; } ret *= M[i][i]; auto inv = M[i][i].inv(); for (int j = i + 1; j < n; ++j) M[i][j] *= inv; for (int h = 0; h < n; ++h) { if (h == i) continue; Fp c = -M[h][i]; for (int j = i + 1; j < n; ++j) M[h][j] += M[i][j] * c; } } return ret; } int main() { cin.tie(nullptr), ios::sync_with_stdio(false); auto Graph = read_input(); int X = get<1>(Graph), Y = get<2>(Graph), Z = get<3>(Graph); auto to = get<4>(Graph); const int N = to.size(); const int V = to.size() + 5, r = V * 2; auto Label = [&](int i) -> int { if (i == X or i == N) return 1; if (i == Y or i == N + 1) return 2; if (i == Z or i == N + 2) return 3; if (i == N + 3) return 4; if (i == N + 4) return 5; return 0; }; auto gen_edge_vec = [&](int i, int j) -> pair>, vector>> { vector b(r), c(r); b[i * 2] = 1, b[j * 2] = -1; c[i * 2 + 1] = 1, c[j * 2 + 1] = -1; if (Label(i)) { b[i * 2] -= 1; b[i * 2 + 1] -= Label(i); } if (Label(j)) { b[j * 2] += 1; b[j * 2 + 1] += Label(j); } vector> bret, cret; for (int i = 0; i < int(b.size()); ++i) { if (b[i] != 0) bret.emplace_back(i, b[i]); if (c[i] != 0) cret.emplace_back(i, c[i]); } return {bret, cret}; }; vector>, vector>, int>> bcws; to.resize(N + 3); for (auto i : to[X]) { to[N].push_back(i); to[i].push_back(N); } for (auto i : to[Y]) { to[N + 1].push_back(i); to[i].push_back(N + 1); } for (auto i : to[Z]) { to[N + 2].push_back(i); to[i].push_back(N + 2); } for (int i = 0; i < N + 3; ++i) { for (int j : to[i]) { if (i > j) continue; auto [b, c] = gen_edge_vec(i, j); bcws.emplace_back(b, c, 1); } if (!Label(i)) { auto [b, c] = gen_edge_vec(i, N + 3); bcws.emplace_back(b, c, 0); } } { auto [b, c] = gen_edge_vec(N + 3, N + 4); bcws.emplace_back(b, c, 0); } vector mat0(r, vector(r)); vector mat1(r, vector(r)); for (const auto &[b, c, w] : bcws) { mint x = rand_int() % mint::mod(); for (auto [i, bi] : b) { for (auto [j, cj] : c) { auto v = bi * cj * x; if (w == 0) { mat0[i][j] += v; mat0[j][i] -= v; } if (w == 1) { mat1[i][j] += v; mat1[j][i] -= v; } } } } for (int t = 0; t < 8; ++t) { std::vector b(r), c(r); for (auto &x : b) x = rand_int() % mint::mod(); for (auto &x : c) x = rand_int() % mint::mod(); for (int i = 0; i < r; ++i) { for (int j = 0; j < r; ++j) mat0[i][j] += b[i] * c[j]; } } std::vector poly_evals; for (int d = 1; d <= N * 2 + 1; ++d) { vector M(r, vector(r)); for (int i = 0; i < r; ++i) { for (int j = 0; j < r; ++j) { M[i][j] = mat0[i][j] + mat1[i][j] * d; } } poly_evals.push_back(determinant(M)); } vector A(poly_evals.size(), vector(poly_evals.size())); for (int i = 0; i < int(poly_evals.size()); ++i) { mint pow = 1; for (int j = 0; j < int(poly_evals.size()); ++j) { A[i][j] = pow; pow *= i + 1; } } A = inverse(A); vector det_poly(poly_evals.size()); for (int i = 0; i < int(poly_evals.size()); ++i) { for (int j = 0; j < int(poly_evals.size()); ++j) det_poly[i] += A[i][j] * poly_evals[j]; } int ret = 0; while (ret < int(det_poly.size()) and det_poly[ret] == 0) ++ret; if (ret < int(det_poly.size())) { cout << ret / 2 << '\n'; } else { cout << "-1\n"; } }