#include #define ll long long #define INF 1000000005 #define MOD 1000000007 #define EPS 1e-10 #define rep(i,n) for(int i=0;i<(int)(n);++i) #define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i) #define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i) #define each(a,b) for(auto& (a): (b)) #define all(v) (v).begin(),(v).end() #define len(v) (int)(v).size() #define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end()) #define cmx(x,y) x=max(x,y) #define cmn(x,y) x=min(x,y) #define fi first #define se second #define pb push_back #define show(x) cout<<#x<<" = "<<(x)< P; typedef pair pll; typedef vector vi; typedef vector vvi; typedef vector vl; typedef vector vvl; typedef vector vd; typedef vector

vp; typedef vector vs; const int MAX_N = 100005; template class ListIterator; template class List { public: using iterator = ListIterator; private: struct block { block *prev, *next; T data; block() : prev(this), next(this){} block(T _data) : prev(this), next(this), data(_data){} block(block *_prev, block *_next) : prev(_prev), next(_next){} }; int N; size_t sz; vector container; friend ListIterator; // cur を nx の前に挿入 iterator insert(block* const nx, block* const cur){ ++sz; cur->prev = nx->prev, cur->next = nx; nx->prev->next = cur, nx->prev = cur; return iterator(cur); } // cur を削除 iterator erase(block* const cur){ --sz; cur->prev->next = cur->next, cur->next->prev = cur->prev; return iterator(cur->next); } public: iterator insert(const iterator nx, const iterator cur){ return insert(nx.ls_ptr, cur.ls_ptr); } iterator insert(const iterator nx, int cur_index){ return insert(nx.ls_ptr, &container[cur_index]); } iterator insert(int next_index, int cur_index){ return iterator(&container[next_index], &container[cur_index]); } iterator erase(const iterator cur){ return erase(cur.ls_ptr); } iterator erase(int cur_index){ return erase(&container[cur_index]); } public: List() : N(0), sz(0){} List(int _N) : N(_N), sz(N), container(_N+1){} List(const vector& _data) : List((int)_data.size()){ build(_data); } List(const List& ls) : N(ls.N), sz(ls.sz), container(ls.container){} void build(const vector& _data){ for(int i = 0; i <= N; i++){ container[i].prev = &container[(i+N)%(N+1)]; container[i].next = &container[(i+1)%(N+1)]; if(i < N) container[i].data = _data[i]; } } void push_back(const T _data){ ++N, ++sz, container.push_back(_data); } void build(){ container.push_back(T()); for(int i = 0; i <= N; i++){ container[i].prev = &container[(i+N)%(N+1)]; container[i].next = &container[(i+1)%(N+1)]; } } friend ostream& operator<< (ostream& os, List& ls){ for(auto& val : ls) os << val << ' '; return os; } const T& operator[](size_t index) const { return container[index].data; } T& operator[](size_t index){ return container[index].data; } size_t size() const { return sz; } bool empty() const { return (size() == 0); } T& front(){ return container[N].next->data; } T& back(){ return container[N].prev->data; } iterator begin(){ return iterator(container[N].next); } iterator end(){ return iterator(&container[N]); } }; template class ListIterator : public std::iterator{ private: friend List; typename List::block *ls_ptr; using base = std::iterator; using value_type = typename base::value_type; using pointer = typename base::pointer; using reference = typename base::reference; private: ListIterator(typename List::block *ls) : ls_ptr(ls){} public: ListIterator(){} ListIterator(const ListIterator& itr) : ls_ptr(itr.ls_ptr){} ListIterator& operator=(const ListIterator& itr) & { return ls_ptr = itr.ls_ptr, *this; } ListIterator& operator=(ListIterator&& itr) & { return ls_ptr = itr.ls_ptr, *this; } reference operator*() const { return ls_ptr->data; } pointer operator->() const { return &(ls_ptr->data); } ListIterator& operator++(){ return ls_ptr = ls_ptr->next, *this; } ListIterator operator++(int){ ListIterator res = *this; return res.ls_ptr = ls_ptr->next, res; } ListIterator& operator--(){ return ls_ptr = ls_ptr->prev, *this; } ListIterator operator--(int){ ListIterator res = *this; return res.ls_ptr = ls_ptr->prev, res; }; bool operator==(const ListIterator& itr) const { return !(*this != itr); }; bool operator!=(const ListIterator& itr) const { return ls_ptr != itr.ls_ptr; } }; // 多重辺はなし class MVC { private: struct edge { int to, rev; }; struct info { // from から to 番目に出ている辺が(を) next の前から消えた(に入れる) int from, to; List::iterator next; info(int ag1, int ag2, List::iterator ag3) : from(ag1), to(ag2), next(ag3){} }; int V, rem_edge_size, fp_size; vector > G; List rem_ver; vector cand, deg; vector > edge_info; set small_deg_ver, use_ver; bool push_cand(int u, int& add_size){ add_size++, cand.push_back(u); return (int)cand.size() < ans_size; } bool erase(int u, bool use, bool alr_use, int& add_size, vector::iterator> >& erase_ver){ if(use && !alr_use){ if(!push_cand(u, add_size)) return false; } erase_ver.emplace_back(u, rem_ver.erase(u)); for(auto& e : G[u]){ edge_info[u].emplace_back(e.to, e.rev, G[e.to].erase(e.rev)); deg[e.to]--, rem_edge_size--; if(deg[e.to] == 0) erase_ver.emplace_back(e.to, rem_ver.erase(e.to)); if(!use){ if(use_ver.count(e.to) == 1) continue; if(!push_cand(e.to, add_size)) return false; if(deg[e.to] > 0) use_ver.insert(e.to); }else{ if(deg[e.to] == 1 && use_ver.count(e.to) == 0) small_deg_ver.insert(e.to); } } return true; } bool erase_rec_set(set& st, bool flag, int& add_size, vector::iterator> >& erase_ver){ while(!st.empty()){ int v = *st.begin(); st.erase(v); if(deg[v] == 0) continue; if(!erase(v, flag, flag, add_size, erase_ver)) return false; } return true; } bool reset(){ small_deg_ver.clear(), use_ver.clear(); return false; } bool erase_rec(int u, bool use, int& add_size, vector::iterator> >& erase_ver){ if(!erase(u, use, false, add_size, erase_ver)) return reset(); while(!small_deg_ver.empty() || !use_ver.empty()){ if(!erase_rec_set(small_deg_ver, false, add_size, erase_ver)) return reset(); if(!erase_rec_set(use_ver, true, add_size, erase_ver)) return reset(); } return true; } bool preprocessing(int K, int& add_size, vector::iterator> >& erase_ver){ for(int u : rem_ver){ if(deg[u] > K){ if(!erase_rec(u, true, add_size, erase_ver)) return false; } } return true; } void postprocessing(int K, int add_size, vector::iterator> >& erase_ver){ if(K == fp_size) return; for(int i = 0; i < add_size; i++){ cand.pop_back(); } for(int i = (int)erase_ver.size() - 1; i >= 0; i--){ auto& p = erase_ver[i]; while(!edge_info[p.first].empty()){ auto& dat = edge_info[p.first].back(); G[dat.from].insert(dat.next, dat.to), deg[dat.from]++, rem_edge_size++; edge_info[p.first].pop_back(); } rem_ver.insert(p.second, p.first); } } bool check(){ if(rem_edge_size == 0){ if((int)cand.size() < ans_size){ ans_size = (int)cand.size(), ans_set = cand; } return false; } return (int)rem_ver.size() > 0; } void transition(int K, int next_ver, bool use){ int pl_add_size = 0; vector::iterator> > pl_erase_ver; if(!erase_rec(next_ver, use, pl_add_size, pl_erase_ver)){ return postprocessing(K-1, pl_add_size, pl_erase_ver); } if(check()) judge(K-1); return postprocessing(K-1, pl_add_size, pl_erase_ver); } int find_max_degree_ver(){ int max_deg = -1, next_ver = -1; for(int v : rem_ver){ if(deg[v] > max_deg) max_deg = deg[v], next_ver = v; } if(2 * rem_edge_size > (long long)max_deg * (int)rem_ver.size()) return -1; return next_ver; } void judge(int K){ int add_size = 0; vector::iterator> > erase_ver; if(!preprocessing(K, add_size, erase_ver)) return postprocessing(K, add_size, erase_ver); if(!check()) return postprocessing(K, add_size, erase_ver); int next_ver = find_max_degree_ver(); if(next_ver < 0) return postprocessing(K, add_size, erase_ver); transition(K, next_ver, true); if((int)cand.size() + (int)G[next_ver].size() < ans_size){ transition(K, next_ver, false); } return postprocessing(K, add_size, erase_ver); } public: vector ans_set; int ans_size; MVC(int node_size) : V(node_size), rem_edge_size(0), G(V), rem_ver(V), deg(V, 0), edge_info(V){ vector _init(V); iota(_init.begin(), _init.end(), 0); rem_ver.build(_init); } void add_edge(int u, int v){ G[u].push_back((edge){v, (int)G[v].size()}); G[v].push_back((edge){u, (int)G[u].size() - 1}); deg[u]++, deg[v]++, rem_edge_size++; } bool solve(int K){ for(int i = 0; i < V; ++i) G[i].build(); fp_size = K, ans_size = fp_size + 1; judge(fp_size); return ans_size <= fp_size; } }; bool used[121]; int main() { cin.tie(0); ios::sync_with_stdio(false); ll S; cin >> S; S = S * 12345LL % 1000003LL; int n = (S % 120) + 2, m = 0; MVC mvc(n); S = S * 12345LL % 1000003LL; ll P = S; rep(i,n){ srep(j,i+1,n){ S = S * 12345LL % 1000003LL; if(S >= P){ mvc.add_edge(i, j); m++; } } } if(m == 0){ cout << "-1\n"; }else{ mvc.solve(n); cout << n - mvc.ans_size + 1 << "\n"; each(v, mvc.ans_set){ used[v] = true; } vector ans; rep(i,n){ if(!used[i]) ans.pb(i); } rep(i,len(ans)-1){ cout << ans[i] + 1 << " "; } cout << ans.back() + 1 << "\n"; } return 0; }