#include "bits/stdc++.h" using namespace std; #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) static const int INF = 0x3f3f3f3f; static const long long INFL = 0x3f3f3f3f3f3f3f3fLL; typedef vector vi; typedef pair pii; typedef vector > vpii; typedef long long ll; template static void amin(T &x, U y) { if(y < x) x = y; } template static void amax(T &x, U y) { if(x < y) x = y; } struct BitSet { enum { K = 2, W = 64 }; uint64_t data[K]; BitSet() : data{} {} explicit operator bool() const { uint64_t r = 0; rep(i, K) r |= data[i]; return r != 0; } bool get(unsigned pos) const { return data[pos / W] >> (pos % W) & 1; } void set(unsigned pos) { data[pos / W] |= uint64_t(1) << (pos % W); } void unset(unsigned pos) { data[pos / W] &= ~(uint64_t(1) << (pos % W)); } int count() const { int res = 0; rep(i, K) res += popcount(data[i]); return res; } BitSet operator&(BitSet that) const { BitSet res; rep(i, K) res.data[i] = data[i] & that.data[i]; return res; } bool isIntersectTo(const BitSet &that) const { return bool(*this & that); } int getSingleton() const { rep(i, K) if(data[i]) { if((data[i] & (data[i] - 1)) != 0) return -1; for(int j = i + 1; j < K; ++ j) if(data[j]) return -1; return i * W + bsf(data[i]); } return -1; } static int bsf(uint64_t x) { #if defined(__GNUC__) return __builtin_ctzll(x); #else unsigned long res; _BitScanForward64(&res, x); return res; #endif } static int popcount(uint64_t x) { #if defined(__GNUC__) return __builtin_popcountll(x); #else return (int)__popcnt64(x); #endif } }; class MaximumCliqueBranchAndBound { public: typedef uint8_t Vertex; BitSet maximumClique(const vector &originalGraph) { graph = originalGraph; int N = (int)graph.size(); levels.assign(N, BitSet()); vertexLevel.assign(N, -1); BitSet initSet; vector> degreeOrder(N); for(int i = 0; i < N; ++ i) { initSet.set(i); degreeOrder[i] = make_pair(-(int)graph[i].count(), i); } sort(degreeOrder.begin(), degreeOrder.end()); numRecs = 0; globalBuffer.resize(N * N + N + N * 2 * N); levelVertices.resize(N); rep(i, N) levelVertices[i].first = globalBuffer.data() + i * N; Vertex *initOrder = globalBuffer.data() + N * N, *nextBuffer = initOrder + N; rep(i, N) initOrder[i] = degreeOrder[i].second; rec(initSet, initOrder, N, nextBuffer); return maxClique; } private: void rec(BitSet remSet, const Vertex *originalOrder, int originalOrderSize, Vertex *buffer) { ++ numRecs; int numLevels = 0, numVertices = 0; for(int ix = 0; ix < originalOrderSize; ++ ix) { int p = originalOrder[ix]; if(!remSet.get(p)) continue; ++ numVertices; int k = 0; while(k < numLevels && levels[k].isIntersectTo(graph[p])) ++ k; if(k == numLevels) { levels[k] = BitSet(); ++ numLevels; } levels[k].set(p); vertexLevel[p] = k; int threshold = maxSize - curSize; if(k > threshold && k == numLevels - 1) { reNumber(p, k, threshold, numLevels); if(!levels[k]) -- numLevels; } } Vertex *order = buffer, *levelOffsets = buffer + numVertices, *nextBuffer = levelOffsets + numLevels; for(int k = 0; k < numLevels; ++ k) levelVertices[k].second = 0; for(int ix = 0; ix < originalOrderSize; ++ ix) { int v = originalOrder[ix]; if(remSet.get(v)) { auto &p = levelVertices[vertexLevel[v]]; p.first[p.second ++] = v; } } numVertices = 0; for(int k = 0; k < numLevels; ++ k) { levelOffsets[k] = numVertices; auto p = levelVertices[k]; for(int i = 0; i < p.second; ++ i) order[numVertices ++] = p.first[i]; } while(1) { int threshold = max(maxSize - curSize, 0); if(threshold >= numLevels || numVertices <= levelOffsets[threshold]) break; int u = order[-- numVertices]; curClique.set(u), ++ curSize; BitSet newSet = remSet & graph[u]; if(newSet) { rec(newSet, order, numVertices, nextBuffer); } else if(curSize > maxSize) { maxClique = curClique, maxSize = curSize; } curClique.unset(u), -- curSize; } } void reNumber(int p, int k, int threshold, int numLevels) { for(int i = 0; i < threshold; ++ i) { BitSet S = graph[p] & levels[i]; int q = S.getSingleton(); if(q == -1) continue; for(int j = i + 1; j <= threshold; ++ j) { if(graph[q] & levels[j]) continue; levels[k].unset(p); levels[i].unset(q); levels[i].set(p); levels[j].set(q); vertexLevel[p] = i; vertexLevel[q] = j; return; } } } vector graph; BitSet curClique, maxClique; int curSize, maxSize; vector levels; vector vertexLevel; vector> levelVertices; vector globalBuffer; long long numRecs; }; //#include "C:\Dropbox\backup\implements\Util\CPUTime.hpp" int main() { int initS; while(~scanf("%d", &initS)) { vector> list; //int initS; for(initS = 1; initS < 1000003; ++initS) { //if(initS % 100 == 0)cerr << initS << "..." << endl; //for(int initS : vector{ 115398, 267904, 52859, 518145, 66814, 519427, 882073, 670079, 758187, 65005, 31884, 519427 , 552242 , 394304 , 371116 , 626395, 60145, 649 }) CPUTIMEIT("test") { int N, P; vector g; { int S = initS; S = ((ll)S * 12345) % 1000003; N = (S % 120) + 2; g.assign(N, BitSet()); S = ((ll)S * 12345) % 1000003; P = S; rep(i, N) reu(j, i + 1, N) { S = ((ll)S * 12345) % 1000003; if(S < P) { g[i].set(j); g[j].set(i); } } } //cerr << initS << " (" << N << ", " << P << ")" << ": "; MaximumCliqueBranchAndBound mc; //double start = getCPUTime(); BitSet ans = mc.maximumClique(g); //list.emplace_back(getCPUTime() - start, initS); if(ans.count() == N) { puts("-1"); } else { printf("%d\n", (int)ans.count() + 1); vector v; rep(i, N) if(ans.get(i)) v.push_back(i); for(int i = 0; i < (int)v.size(); ++ i) { if(i != 0) putchar(' '); printf("%d", v[i] + 1); } puts(""); } } return 0; }