#include #define N_MAX 100 #define M_MAX 5000 typedef struct Edge { struct Edge *next; int v; unsigned int label; } edge; void chmin(int* a, int b) { if (*a > b) *a = b; } #define MT_N 624 #define MT_M 397 #define MT_MATRIX_A 0x9908b0dfUL #define MT_UPPER_MASK 0x80000000UL #define MT_LOWER_MASK 0x7fffffffUL static unsigned int mt[MT_N]; static int mti = MT_N + 1; void init_genrand(unsigned int s) { mt[0] = s & 0xffffffffUL; for (mti = 1; mti < MT_N; mti++) { mt[mti] = (1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti); mt[mti] &= 0xffffffffUL; } } unsigned int genrand() { unsigned int y; static unsigned int mag01[2] = {0x0UL, MT_MATRIX_A}; if (mti >= MT_N) { int kk; if (mti == MT_N + 1) init_genrand(5489UL); for (kk = 0; kk < MT_N - MT_M; kk++) { y = (mt[kk] & MT_UPPER_MASK) | (mt[kk+1] & MT_LOWER_MASK); mt[kk] = mt[kk+MT_M] ^ (y >> 1) ^ mag01[y&0x1UL]; } for (; kk < MT_N - 1; kk++) { y = (mt[kk] & MT_UPPER_MASK) | (mt[kk+1] & MT_LOWER_MASK); mt[kk] = mt[kk+(MT_M-MT_N)] ^ (y >> 1) ^ mag01[y&0x1UL]; } y = (mt[MT_N-1] & MT_UPPER_MASK) | (mt[0] & MT_LOWER_MASK); mt[MT_N-1] = mt[MT_M-1] ^ (y >> 1) ^ mag01[y&0x1UL]; mti = 0; } y = mt[mti++]; y ^= (y >> 11); y ^= (y << 7) & 0x9d2c5680UL; y ^= (y << 15) & 0xefc60000UL; y ^= (y >> 18); return y; } #define POWX 3 // 3 -> 2^8, 4 -> 2^16, 5 -> 2^32 const unsigned int powd[5] = {2, 4, 16, 256, 65536}, powe[5] = {1, 2, 4, 8, 16}; // Multiplication on a finite field of size 2^32 with XOR addition unsigned int nim_product(unsigned int A, unsigned int B) { if (A > B) return nim_product(B, A); else if (A <= 1) return A * B; static unsigned int memo[256][256] = {}; if (B < 256 && memo[A][B] != 0) return memo[A][B]; int i; for (i = 0; i < POWX; i++) { if (B == powd[i]) { if (A == powd[i]) return (B >> 1) * 3; else return A * B; } } unsigned int a[2], b[2], ans[2][2]; for (i = POWX - 1; i >= 0; i--) if (B > powd[i]) break; a[1] = A & (powd[i] - 1); a[0] = (A ^ a[1]) >> powe[i]; b[1] = B & (powd[i] - 1); b[0] = (B ^ b[1]) >> powe[i]; ans[0][0] = nim_product(a[0], b[0]); ans[0][1] = nim_product(a[0], b[1]); ans[1][0] = nim_product(a[1], b[0]); ans[1][1] = nim_product(a[1], b[1]); if (B < 256) { memo[A][B] = (ans[0][0] ^ ans[0][1] ^ ans[1][0]) * powd[i] ^ nim_product(ans[0][0], powd[i] >> 1) ^ ans[1][1]; return memo[A][B]; } else return (ans[0][0] ^ ans[0][1] ^ ans[1][0]) * powd[i] ^ nim_product(ans[0][0], powd[i] >> 1) ^ ans[1][1]; } // Solution example (O(N^4) time by cumulative sum) int solve4_2(int N, int M, int X, int Y, int Z, int A[], int B[]) { static int i, u, w, adj_mat[N_MAX + 1][N_MAX + 1]; static edge *adj[N_MAX + 1], e[M_MAX * 2], *p, *pp; for (u = 1; u <= N; u++) for (w = u + 1; w <= N; w++) adj_mat[u][w] = 0; for (i = 1; i <= M; i++) { u = A[i]; w = B[i]; adj_mat[u][w] = 1; } for (u = 1; u <= N; u++) adj[u] = NULL; for (u = 1, i = 0; u <= N; u++) { for (w = u + 1; w <= N; w++) { if (adj_mat[u][w] != 0) continue; e[i].v = w; e[i].label = genrand() % (powd[POWX] - 1) + 1; e[i].next = adj[u]; adj[u] = &(e[i++]); e[i].v = u; e[i].label = e[i-1].label; e[i].next = adj[w]; adj[w] = &(e[i++]); } } static int k, kk, l, x, y, z, cur, prev; static unsigned int dp[2][4][N_MAX + 1][N_MAX + 1][N_MAX + 1], tmp; for (k = 0; k < 4; k++) { for (p = adj[X]; p != NULL; p = p->next) { for (u = 1; u <= N; u++) { for (pp = adj[u]; pp != NULL; pp = pp->next) { dp[0][k][p->v][u][pp->v] = 0; dp[1][k][p->v][u][pp->v] = 0; } } } } for (p = adj[X]; p != NULL; p = p->next) { u = p->v; k = (u == Y)? 1: (u == Z)? 2: 0; dp[0][k][u][X][u] = p->label; } for (l = 2, cur = 1, prev = 0; l <= N; l++, cur ^= 1, prev ^= 1) { for (k = 0; k < 4; k++) { for (p = adj[X]; p != NULL; p = p->next) { w = p->v; for (y = 1; y <= N; y++) { for (pp = adj[y], tmp = 0; pp != NULL; pp = pp->next) { x = pp->v; tmp ^= dp[prev][k][w][x][y]; } for (pp = adj[y]; pp != NULL; pp = pp->next) { z = pp->v; kk = k | ((z == Y)? 1: (z == Z)? 2: 0); if ((z == X && kk != 3) || (z == Y && (k & 1) != 0) || (z == Z && (k & 2) != 0)) continue; if (y == X || y == Y || y == Z) dp[cur][kk][w][y][z] ^= nim_product(tmp ^ dp[prev][k][w][z][y], pp->label); else dp[cur][kk][w][y][z] ^= nim_product(tmp, pp->label); dp[prev][k][w][z][y] = 0; } } } } for (p = adj[X]; p != NULL; p = p->next) { for (pp = p->next; pp != NULL; pp = pp->next) if (dp[cur][3][p->v][pp->v][X] != 0) break; if (pp != NULL) break; } if (p != NULL) break; } if (l > N) return -1; else return l; } int main() { int i, N, M, X, Y, Z, A[M_MAX + 1], B[M_MAX + 1], ans[2]; scanf("%d %d", &N, &M); scanf("%d %d %d", &X, &Y, &Z); for (i = 1; i <= M; i++) scanf("%d %d", &(A[i]), &(B[i])); ans[0] = solve4_2(N, M, X, Y, Z, A, B); // ans[1] = solve4_2(N, M, X, Y, Z, A, B); // chmin(&(ans[0]), ans[1]); printf("%d\n", (ans[0] > N)? -1: ans[0]); fflush(stdout); return 0; }