#include #include #include #include #include #include #include #include #include #include #include #define _fetch(_1, _2, _3, _4, name, ...) name #define rep2(i, n) rep3(i, 0, n) #define rep3(i, a, b) rep4(i, a, b, 1) #define rep4(i, a, b, c) for (int i = int(a); i < int(b); i += int(c)) #define rep(...) _fetch(__VA_ARGS__, rep4, rep3, rep2, _)(__VA_ARGS__) using namespace std; using i64 = long long; using u8 = unsigned char; using u32 = unsigned; using u64 = unsigned long long; using f80 = long double; using u128 = __uint128_t; const u32 N_MAX = 120; int degs[N_MAX + 1]; u128 V_deg[N_MAX + 2]; u128 edges[N_MAX + 1]; inline int ctz(u128 n) { if (u64(n)) return __builtin_ctzll(u64(n)); else return 64 + __builtin_ctzll(u64(n >> 64)); } inline int pop_count(u128 n) { if (u64(n)) return __builtin_popcountll(u64(n)); else return __builtin_popcountll(u64(n)) + __builtin_popcountll(u64(n >> 64)); } inline void delete_v(u128 G, int v) { auto Nv = edges[v] & G; while (Nv) { auto fy = Nv & -Nv; int y = ctz(fy); V_deg[degs[y]--] ^= fy; V_deg[degs[y]] ^= fy; Nv ^= fy; } } inline void insert_v(u128 G, int v) { auto Nv = edges[v] & G; while (Nv) { auto fy = Nv & -Nv; int y = ctz(fy); V_deg[degs[y]++] ^= fy; V_deg[degs[y]] ^= fy; Nv ^= fy; } } inline void delete_Nv(u128 G, int v) { auto fv = u128(1) << v; auto Nv = fv ^ (edges[v] & G); while (Nv) { auto fy = Nv & -Nv; int y = ctz(fy); delete_v(G, y); Nv ^= fy; } } inline void insert_Nv(u128 G, int v) { auto fv = u128(1) << v; auto Nv = fv ^ (edges[v] & G); while (Nv) { auto fy = Nv & -Nv; int y = ctz(fy); insert_v(G, y); Nv ^= fy; } } // Naive: O(3^(n/3)) ~= O(1.4422^n) int mis1(u128 G) { if (G == 0) return 0; for (int deg = 0; ; ++deg) if (V_deg[deg] & G) { int i_max = 0; auto fv = V_deg[deg] & G; fv &= -fv; int v = ctz(fv); auto Nv = (fv ^ edges[v]) & G; while (Nv) { auto fy = Nv & -Nv; int y = ctz(fy); auto Ny = (fy ^ edges[y]) & G; delete_v(G, y); i_max = max(i_max, mis1(G ^ Ny)); insert_v(G, y); Nv ^= fy; } return 1 + i_max; } } // P(v, is_clique) using P = pair; inline P max_deg_vertex(u128 G, u128 S, int beg) { for (int deg = beg; ; ++deg) { u128 Vd = V_deg[deg] & G; if ((S |= Vd) != G) continue; auto fv = Vd & -Vd; int v = ctz(fv); return P(v, (Vd == G) && (pop_count(G) == deg + 1)); } } int vertices[N_MAX]; // O(1.2905^n) int mis3(u128 G, int idx=0) { if (G == 0) return 0; // d(v) <= 1 const u128 V01 = (V_deg[0] | V_deg[1]) & G; if (V01) { auto fv = V01 & -V01; int v = ctz(fv); auto Nv = fv ^ (edges[v] & G); delete_Nv(G, v); vertices[idx] = v; int ret = 1 + mis3(G ^ Nv, idx + 1); insert_Nv(G, v); return ret; } // d(v) >= 3 const u128 V2 = V_deg[2] & G; if (V2 != G) { auto p = max_deg_vertex(G, V2, 3); auto v = p.first; auto fv = u128(1) << v; if (p.second == true) { vertices[idx++] = v; return 1; } else { int vertices_back[N_MAX]; // G / v delete_v(G, v); int ret = mis3(G ^ fv, idx); copy(vertices + idx, vertices + idx + ret, vertices_back); insert_v(G, v); // G / N(v) auto Nv = fv ^ (edges[v] & G); delete_Nv(G, v); vertices[idx] = v; int ret2 = 1 + mis3(G ^ Nv, idx + 1); insert_Nv(G, v); if (ret > ret2) { copy(vertices_back, vertices_back + ret, vertices + idx); } else { ret = ret2; } return ret; } } // Delta(G) = delta(G) = 2 int ret = 0; while (G) { auto fv = G & -G; int cycle_len = 0; for (; fv; ++cycle_len) { int v = ctz(fv); G ^= fv; fv = edges[v] & G; fv &= -fv; if (cycle_len & 1) vertices[idx++] = v; } ret += cycle_len / 2; } return ret; } struct Rand { Rand(u32 seed) : x(seed) {} u32 next() { return x = u64(x) * 12345 % 1000003; } u32 x; }; u128 set_graph(int S) { auto gene = Rand(S); int N = gene.next() % N_MAX + 2; int P = gene.next(); // fprintf(stderr, "N: %u, P: %u\n", N, P); rep(i, N) { degs[i] = V_deg[i] = edges[i] = 0; } rep(i, N) rep(j, i + 1, N) { int X = gene.next(); if (X >= P) { edges[i] |= u128(1) << j; degs[i]++; edges[j] |= u128(1) << i; degs[j]++; // fprintf(stderr, "E: %u <-> %u (%u)\n", i, j, X); } } rep(i, N) V_deg[degs[i]] |= u128(1) << i; u128 G = (u128(1) << N) - 1; return G; } void solve() { int S; while (~scanf("%d", &S)) { u128 G = set_graph(S); int len = mis3(G); if (len == pop_count(G)) { puts("-1"); } else { printf("%u\n", len + 1); rep(i, len) { if (i) putchar(' '); printf("%u", vertices[i] + 1); } puts(""); } } } int main() { clock_t beg = clock(); solve(); clock_t end = clock(); fprintf(stderr, "%.3f sec\n", double(end - beg) / CLOCKS_PER_SEC); return 0; }