template<typename T> class ListIterator;

template<typename T>
class List {
public:
    using iterator = ListIterator<T>;

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<block> container;
    friend ListIterator<T>;
    // 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<T>& _data) : List((int)_data.size()){ build(_data); }
    List(const List& ls) : N(ls.N), sz(ls.sz), container(ls.container){}
    void build(const vector<T>& _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<typename T>
class ListIterator {
private:
    friend List<T>;
    typename List<T>::block *ls_ptr;
    using iterator_category = std::bidirectional_iterator_tag;
    using value_type = T;
    using difference_type = T;
    using pointer = T*;
    using reference = T&;

private:
    ListIterator(typename List<T>::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 MIS {
private:
    struct edge {
        int to, rev;
    };
    struct info {
        int from, to;
        List<edge>::iterator next;
        info(int ag1, int ag2, List<edge>::iterator ag3) :
            from(ag1), to(ag2), next(ag3){}
    };

    using LL = unsigned __int128;

    int V;
    vector<List<edge> > G;
    List<int> rem_ver;
    vector<int> cand, deg, is_rem;
    vector<vector<info> > edge_info;
    LL not_use_ver;

    int get_first_element(LL num){
        int x = __builtin_ffsll(num & 0xffffffffffffffff);
        int y = __builtin_ffsll((num >> 64) & 0xffffffffffffffff);
        return x ? (x - 1) : (y + 63);
    }
    bool finish(){
        return (int)cand.size() + (int)rem_ver.size() <= ans_size;
    }
    bool erase(int u, bool use, bool alr_use, int& add_size, vector<pair<int, List<int>::iterator> >& erase_ver){
        erase_ver.emplace_back(u, rem_ver.erase(u)), is_rem[u] = 0;
        if(use && !alr_use){
            add_size++, cand.push_back(u);
        }else{
            if(finish()) return false;
        }
        for(auto& e : G[u]){
            edge_info[u].emplace_back(e.to, e.rev, G[e.to].erase(e.rev)), deg[e.to]--;
            if(deg[e.to] == 0) erase_ver.emplace_back(e.to, rem_ver.erase(e.to)), is_rem[e.to] = 0;
            if(use){
                if(deg[e.to] > 0) not_use_ver |= ((LL)1 << e.to);
            }else if((not_use_ver >> e.to & 1) == 0 && deg[e.to] == 0){
                add_size++, cand.push_back(e.to);
            }
        }
        return !finish();
    }
    bool erase_rec_set(bool flag, int& add_size, vector<pair<int, List<int>::iterator> >& erase_ver){
        while(not_use_ver != 0){
            int v = get_first_element(not_use_ver);
            not_use_ver ^= ((LL)1 << v);
            if(deg[v] == 0) continue;
            if(!erase(v, flag, flag, add_size, erase_ver)) return false;
        }
        return true;
    }
    bool erase_rec(int u, bool use, int& add_size, vector<pair<int, List<int>::iterator> >& erase_ver){
        if(!erase(u, use, false, add_size, erase_ver)){
            not_use_ver = 0;
            return false;
        }
        while(not_use_ver != 0){
            if(!erase_rec_set(false, add_size, erase_ver)){
                not_use_ver = 0;
                return false;
            }
        }
        return true;
    }
    bool preprocessing(int& add_size, vector<pair<int, List<int>::iterator> >& erase_ver){
        for(int u : rem_ver){
            if(is_rem[u] == 1 && deg[u] <= 1){
                if(!erase_rec(u, true, add_size, erase_ver)) return false;
            }
        }
        return true;
    }
    void postprocessing(int& add_size, vector<pair<int, List<int>::iterator> >& erase_ver){
        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]++;
                edge_info[p.first].pop_back();
            }
            rem_ver.insert(p.second, p.first), is_rem[p.first] = 1;
        }
    }
    bool check(){
        if(rem_ver.empty()){
            if((int)cand.size() > ans_size){
                ans_size = (int)cand.size(), ans_set = cand;
            }
            return false;
        }
        return true;
    }
    void transition(int next_ver, bool use){
        int pl_add_size = 0;
        vector<pair<int, List<int>::iterator> > pl_erase_ver;
        if(!erase_rec(next_ver, use, pl_add_size, pl_erase_ver)){
            return postprocessing(pl_add_size, pl_erase_ver);
        }
        if(check()) judge();
        return postprocessing(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;
        }
        return next_ver;
    }
    void judge(){
        int add_size = 0;
        vector<pair<int, List<int>::iterator> > erase_ver;
        if(!preprocessing(add_size, erase_ver)) return postprocessing(add_size, erase_ver);
        if(!check()) return postprocessing(add_size, erase_ver);
        int next_ver = find_max_degree_ver();
        transition(next_ver, true);
        if(deg[next_ver] > 1 && (int)cand.size() + (int)rem_ver.size() > ans_size + 1){
            transition(next_ver, false);
        }
        return postprocessing(add_size, erase_ver);
    }
public:
    vector<int> ans_set;
    int ans_size;

    MIS(int node_size) :
        V(node_size), G(V), rem_ver(V), deg(V, 0), is_rem(V, 1), edge_info(V), not_use_ver(0), ans_size(0){
        vector<int> _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]++;
    }
    int solve(){
        for(int i = 0; i < V; ++i) G[i].build();
        judge();
        return ans_size;
    }
};