#include<bits/stdc++.h>
#include<atcoder/all>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx2")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define rep(i,n) for(ll i = 0LL; i < (ll)n; ++i)
#define rep1(i,n) for(ll i = 1LL; i <= (ll)n; ++i)
#define rep2(i,m,n) for(ll i = (ll)m; i < (ll)n; ++i)
#define rrep(i,n) for(ll i = (ll)n - 1; i >= 0LL; --i)
#define rrep1(i,n) for(ll i = (ll)n; i > 0LL; --i)
#define rrep2(i,m,n) for(ll i = (ll)m; i > (ll)n; --i)
#define lb(a,x) static_cast<ll>(lower_bound(all(a), x) - a.begin())
#define ub(a,x) static_cast<ll>(upper_bound(all(a), x) - a.begin())
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define SORT(a) sort(all(a));
#define RSORT(a) sort(rall(a));
#define REV(a) reverse(all(a));
#define CEIL(x,y) (x+y-1)/y
#define pb push_back
#define eb emplace_back
#define _GLIBCXX_DEBUG
#define _CRT_SECURE_NO_WARNINGS
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)

using namespace std;
using namespace chrono;
using namespace atcoder;

using ld = long double;
using ll = long long;
using ull = unsigned long long;

using vi = vector<int>;
using vl = vector<ll>;
using vc = vector<char>;
using vb = vector<bool>;
using vs = vector<string>;

using vvi = vector<vi>;
using vvl = vector<vl>;
using vvc = vector<vc>;
using vvb = vector<vb>;
using vvs = vector<vs>;


using pii = pair<int, int>;
using pll = pair<ll, ll>;

using si = set<int>;
using sl = set<ll>;

using mii = map<int, int>;
using mll = map<ll, ll>;

//in
void in(){}
template<class T>void in(vector<T> &v){
    for(T &t : v)cin >> t;
}
template<class T>void in(vector<vector<T>> &v){
    for(auto &row : v)for(T&element : row)cin >> element;
}
template<class Head, class... Tail>void in(Head &head, Tail &...tail){
    cin >> head; in(tail...);
}

//out
void out(){}
template<class T>void out(const T &t){
    cout << t << endl;
}
template<class T>void out(vector<T> &v){
    for(T &t : v)cout << t << ' ';
    cout << endl;
}
template<class T>void out(vector<vector<T>> &v){
    for(vector<T> &row : v){
        for(T &element : row){
            cout << element << ' ';
        }
        cout << endl;
    }
}
template<class Head, class...Tail>void out(const Head &head, const Tail &...tail){
    cout << head; out(tail...);
}

//chmax
template<typename T>bool chmax(T &a, T b){
    return((a < b)? (a = b, true) : (false));
}

//chmin
template<typename T>bool chmin(T &a, T b){
    return((a > b)? (a = b, true) : (false));
}

//min
template<typename T>T MIN(vector<T> &v){
    T mn = numeric_limits<T>::max();
    for(T &e : v){
        mn = min(mn, e);
    }
    return mn;
}

//max
template<typename T>T MAX(vector<T> &v){
    T mx = numeric_limits<T>::min();
    for(T &e : v){
        mx = max(mx, e);
    }
    return mx;
}

//sum
template<typename T>T SUM(vector<T> &v){
    T sum = 0;
    for(T &e : v){
        sum += e;
    }
    return sum;
}

//l_sort
template<typename T>void l_sort(vector<T> &l, vector<T> &r){
    assert(l.size() == r.size());
    long long n = l.size();
    vector<pair<T, T>> p;
    for(ll i = 0; i < n; i++){
        p.emplace_back(l[i], r[i]);
    }
    sort(p.begin(), p.end());
    for(ll i = 0; i < n; i++){
        l[i] = p[i].first;
        r[i] = p[i].second;
    }
}

//r_sort
template<typename T>void r_sort(vector<T> &l, vector<T> &r){
    assert(l.size() == r.size());
    long long n = l.size();
    vector<pair<T, T>> p;
    for(ll i = 0; i < n; i++){
        p.emplace_back(r[i], l[i]);
    }
    sort(p.begin(), p.end());
    for(ll i = 0; i < n; i++){
        l[i] = p[i].second;
        r[i] = p[i].first;
    }
}
//-----------------------array-----------------------//
//cumulative_sum
template<typename T> vector<T> cumulative_sum(vector<T> &v){
    ll n = v.size();
    vector<T> res(n + 1);
    for(ll i = 0; i < n; ++i){
        res[i + 1] = res[i] + v[i];
    }
    return res;
}

//LCS
ll LCS(string s, string t){
    vector dp(s.size() + 1,vector<ll>(t.size() + 1));
    rep(i,s.size()){
        rep(j,t.size()){
            if(s[i] == t[j]){
                dp[i + 1][j + 1] = max({dp[i][j + 1],dp[i + 1][j],dp[i][j] + 1});
            }else{
                dp[i + 1][j + 1] = max(dp[i][j + 1],dp[i + 1][j]);
            }
        }
    }
    return dp[s.size()][t.size()];
}

//LIS
template<typename T>ll LIS(vector<T> &a){
    vector<T> dp;
	for (T &e : a){
		auto it = lower_bound(dp.begin(), dp.end(), e);
		if (it == dp.end()){
			dp.push_back(e);
		}else{
			*it = e;
		}
	}
	return (ll)dp.size();
}

template< typename T > struct Compress {
    vector< T > xs;

    Compress() = default;

    Compress(const vector< T > &vs) {
        add(vs);
    }

    Compress(const initializer_list< vector< T > > &vs) {
        for(auto &p : vs) add(p);
    }

    void add(const vector< T > &vs) {
        copy(begin(vs), end(vs), back_inserter(xs));
    }

    void add(const T &x) {
        xs.emplace_back(x);
    }

    void build() {
        sort(begin(xs), end(xs));
        xs.erase(unique(begin(xs), end(xs)), end(xs));
    }

    vector< ll > get(const vector< T > &vs) const {
        vector< ll > ret;
        transform(begin(vs), end(vs), back_inserter(ret), [&](const T &x) {
            return lower_bound(begin(xs), end(xs), x) - begin(xs);
        });
        return ret;
    }

    ll get(const T &x) const {
        return lower_bound(begin(xs), end(xs), x) - begin(xs);
    }

    const T &operator[](ll k) const {
        return xs[k];
    }
};

ll edit_distance(string &s, string &t){
    ll n = s.size(), m = t.size();
    vector dp(n + 1, vector<ll>(m + 1));
    for(ll i = 1; i <= n; i++)dp[i][0] = i;
    for(ll j = 1; j <= m; j++)dp[0][j] = j;
    for(ll i = 1; i <= n; i++)for(ll j = 1; j <= m; j++){
        dp[i][j] = min({dp[i - 1][j] + 1, dp[i][j - 1] + 1, dp[i - 1][j - 1] + (s[i - 1] == t[j - 1]? 0 : 1)});
    }
    return dp[n][m];
}
//--------------------data_structure-----------------//
//suffix_array
struct suffix_array{
    vector<ll> sa, rank, tmp;
    ll n;
    string base;

    //suffix_arrayを構築
    suffix_array(const string s){
        n = s.size();
        base = s;
        sa.resize(n);
        rank.resize(n);
        tmp.resize(n);

        for(ll i = 0; i < n; i++){
            sa[i] = i;
            rank[i] = s[i];
        }

        for(ll k = 1; k < n; k *= 2){
            auto compare_sa = [&](ll i, ll j){
                if(rank[i] != rank[j])return rank[i] < rank[j];
                ll ri = (i + k < n) ? rank[i + k] : -1;
                ll rj = (j + k < n) ? rank[j + k] : -1;
                return ri < rj;
            };
            sort(sa.begin(), sa.end(), compare_sa);

            tmp[sa[0]] = 0;
            for(ll i = 1; i < n; i++){
                tmp[sa[i]] = tmp[sa[i - 1]] + (compare_sa(sa[i - 1], sa[i])? 1 : 0);
            }
            rank = tmp;
        }
    }

    //部分文字列の個数を求める
    ll get_counts(string t){
        string u = t + "彁";
        ll num1, num2;
        {
            ll m = t.size();
            ll ng = -1, ok = n;
            while(ok - ng > 1){
                ll mid = (ng + ok) / 2;
                ll l = sa[mid];
                if(base.substr(l, m) >= t){
                    ok = mid;
                }else{
                    ng = mid;
                }
            }
            num1 = ok;
        }
        {
            ll m = u.size();
            ll ng = -1, ok = n;
            while(ok - ng > 1){
                ll mid = (ng + ok) / 2;
                ll l = sa[mid];
                if(base.substr(l, m) >= u){
                    ok = mid;
                }else{
                    ng = mid;
                }
            }
            num2 = ok;
        }
        return num2 - num1;
    }
};
//-----------------------check-----------------------//
//is_prime
template<typename T> bool is_prime(T n){
    if(n <= 1)return false;
    T m = sqrt(n);
    for(ll i = 2; i <= m; ++i){
        if(n % i == 0)return false;
    }
    return true;
}

//is_square
template<typename T> bool is_square(T n){
    if(n < 0)return false;
    T m = sqrt(n);
    if(n == m * m){
        return true;
    }else{
        return false;
    }
}

//is_substring
bool is_substring(const string& s, const string& t){
    const ll n = s.size(), m = t.size();
    for(ll i = 0; i + m <= n; ++i){
        if(s.substr(i, m) == t)return true;
    }
    return false;
}
//-----------------------math------------------------//
//gcd(faster)
ll GCD(ll A, ll B){
    if(B == 0){
        return A;
    }else{
        return GCD(B, A % B);
    }
}

//lcm(faster)
ll LCM(ll A, ll B){
    return A / GCD(A, B) * B;
}

//comb
ll comb(ll n, ll r){
    assert(n >= 2);
    vector dp(n + 1, vector<ll>(r + 1));
    for(ll i = 0; i < n + 1; ++i){
        dp[i][0] = 1;
    }
    for(ll i = 0; i < r + 1; ++i){
        dp[i][i] = 1;
    }
    for(ll i = 1; i < n + 1; ++i){
        for(ll j = 1; j < min(i, r + 1); ++j){
            dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j];
        }
    }
    return dp[n][r];
}

// comb_mod
using mint_comb = atcoder::static_modint<1000000007>;

vector<mint_comb> fac, finv, inv;

// テーブルを作る前処理
void init_comb_mod(ll size) {
    size += 109;
    fac.resize(size);
    finv.resize(size);
    inv.resize(size);
    const ll MOD = mint_comb::mod();
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (ll i = 2; i < size; i++){
        fac[i] = fac[i - 1] * i;
        inv[i] = MOD - inv[MOD%i] * (MOD / i);
        finv[i] = finv[i - 1] * inv[i];
    }
}

// 二項係数計算
mint_comb comb_mod(ll n, ll k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * finv[k] * finv[n - k];
}

//make_random
//long long
ll rand_ll(ll l, ll r){
    if(l > r)swap(l, r);
    random_device rd;
    mt19937_64 gen(rd());
    uniform_int_distribution<ll>dis(l, r);
    return dis(gen);
}

//int
int rand_int(int l, int r){
    if(l > r)swap(l, r);
    return l + rand() % (r - l + 1);
}

//double
ld rand_double(){
    return (ld)1.0 * rand() / RAND_MAX;
}

//base_conversion
ll ntodec(const char c){
    if(c >= '0' && c <= '9'){
        return (ll)c - '0';
    }else{
        return (ll)c - 55;
    }
}
char decton(const ll n){
    if(n >= 0 && n <= 9){
        return (char)'0' + n;
    }else{
        return (char)55 + n;
    }
}
inline ll pow_ll(ll x,ll n){
    ll ret = 1;
    rep(i,n){
        ret *= x;
    }
    return ret;
}
string base_conversion(string str, ll n, ll m){
    ull tmp = 0;
    string ret;
    rep(i,str.size()){
        tmp += (ull)ntodec(str[str.size() - 1 - i]) * pow_ll(n, i);
    }
    if(tmp == 0){
        return "0";
    }
    while(tmp != 0){
        ret = decton(tmp % m) + ret;
        tmp /= m;
    }
    return ret;
}

//calc_triangle
long double calc_triangle(long double x1,long double y1,long double x2,long double y2,long double x3,long double y3){
    return abs((x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)) / 2.0);
}

//文字列の最小周期
vector<ll> computeLPSArray(const string& pattern) {
    ll m = pattern.length();
    vector<ll> lps(m);
    ll len = 0;
    lps[0] = 0;
    ll i = 1;
    while (i < m) {
        if (pattern[i] == pattern[len]) {
            len++;
            lps[i] = len;
            i++;
        } else {
            if (len != 0) {
                len = lps[len - 1];
            } else {
                lps[i] = 0;
                i++;
            }
        }
    }
    return lps;
}
ll findMinimumPeriod(const string& str) {
    ll n = str.length();
    vector<ll> lps = computeLPSArray(str);
    ll len = lps[n - 1];
    ll period = n - len;
    if (n % period == 0) {
        return period;
    } else {
        return n;
    }
}
//-----------------------graph-----------------------//
//graph_template
struct Edge{
    ll to;
    ll cost;
    Edge(ll to, ll cost) : to(to), cost(cost) {}
    bool operator>(const Edge &e) const{
        return cost > e.cost;
    }
    bool operator<(const Edge &e) const{
        return cost < e.cost;
    }
};

struct Edge2{
    ll from;
    ll to;
    ll cost;
    Edge2(ll from, ll to, ll cost) : from(from), to(to), cost(cost) {}
    bool operator>(const Edge2 &e) const{
        return cost > e.cost;
    }
    bool operator<(const Edge2 &e) const{
        return cost < e.cost;
    }
};

struct Edge3 {
    ll to;
    Edge3(ll to) : to(to) {}
};

struct Graph{
    Graph() = default;
    vector<vector<Edge>> G;

    Graph(ll N){
        G.resize(N);
    }

    ll size(){
        return G.size();
    }

    void add_edge(ll from, ll to, ll cost = 1){
        G[from].push_back(Edge(to, cost));
        G[to].push_back(Edge(from, cost));
    }

    void add_directed_edge(ll from, ll to, ll cost = 1){
        G[from].push_back(Edge(to, cost));
    }

    vector<Edge> &operator[](ll v){
        return G[v];
    }
};

//dijkstra
struct dijkstra{
    vector<ll> dist;
    vector<ll> prev;

    //dijkstraを構築
    dijkstra(Graph &G, ll s){
        ll N = G.size();
        dist.assign(N, 1LL << 60);
        prev.assign(N, -1);
        priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>>> pq;
        dist[s] = 0;
        pq.emplace(dist[s], s);
        while (!pq.empty()){
            auto p = pq.top();
            pq.pop();
            ll v = p.second;
            if(dist[v] < p.first)continue;
            for (auto &e : G[v]){
                if (dist[e.to] > dist[v] + e.cost){
                    dist[e.to] = dist[v] + e.cost;
                    prev[e.to] = v;
                    pq.emplace(dist[e.to], e.to);
                }
            }
        }
    }

    //最小コストを求める
    ll get_cost(ll to){
        return dist[to];
    }

    //最短経路を求める
    vector<ll> get_path(ll to){
        vector<ll> get_path;
        for (ll i = to; i != -1; i = prev[i]){
            get_path.push_back(i);
        }
        reverse(get_path.begin(), get_path.end());
        return get_path;
    }

    //到達可能か調べる
    bool cango(ll to){
        return dist[to] != 1LL << 60;
    }
};

//bellman_ford
struct bellman_ford{
    vector<ll> dist;
    vector<ll> prev;
    ll start;
    ll n;
    bool cl = false;

    //bellman_fordを構築
    bellman_ford(Graph &g, ll s){
        start = s;
        n = g.size();
        dist.assign(n, 1LL << 60);
        prev.assign(n, -1);
        vector<ll> counts(n);
        vector<bool> inqueue(n);

        queue<ll> q;
        dist[s] = 0;
        q.push(s);
        inqueue[s] = true;

        while(!q.empty()){
            ll from = q.front();
            q.pop();
            inqueue[from] = false;

            for(auto &e : g[from]){
                ll d = dist[from] + e.cost;
                if(d < dist[e.to]){
                    dist[e.to] = d;
                    prev[e.to] = from;
                    if(!inqueue[e.to]){
                        q.push(e.to);
                        inqueue[e.to] = true;
                        ++counts[e.to];

                        if(n < counts[e.to])cl = true;
                    }
                }
            }
        }
    }

    //最小コストを求める
    ll get_cost(ll to){
        return dist[to];
    }

    //最短経路を求める
    vector<ll> get_path(ll to){
        vector<ll> path;
        if(dist[to] != 1LL << 60){
            for(ll i = to; i != -1; i = prev[i]){
                path.push_back(i);
            }
            reverse(path.begin(), path.end());
        }
        return path;
    }

    //到達可能か調べる
    bool cango(ll to){
        return (dist[to] != 1LL << 60);
    }

    //負の閉路の有無を調べる
    bool closed(){
        return cl;
    }
};

//warshall_floyd
struct warshall_floyd{
    vector<vector<ll>> d;
    vector<vector<ll>> next;
    bool cl = false;

    //warshall_floydを構築
    warshall_floyd(Graph &g){
        ll n = g.size();
        d.resize(n, vector<ll>(n, 1LL << 60));
        next.resize(n, vector<ll>(n, -1));

        for(ll i = 0; i < n; i++){
            d[i][i] = 0;
        }

        for(ll i = 0; i < n; i++){
            for(auto e : g[i]){
                d[i][e.to] = e.cost;
                next[i][e.to] = e.to;
            }
        }

        for(ll k = 0; k < n; ++k){
            for(ll i = 0; i < n; ++i){
                for(ll j = 0; j < n; ++j){
                    if(d[i][k] == 1LL << 60 || d[k][j] == 1LL << 60)continue;
                    if(d[i][j] > d[i][k] + d[k][j]){
                        d[i][j] = d[i][k] + d[k][j];
                        next[i][j] = next[i][k];
                    }
                }
            }
        }

        for(ll i = 0; i < n; i++){
            if(d[i][i] < 0){
                cl = true;
                break;
            }
        }
    }

    //最小コストを求める
    ll get_cost(ll from, ll to){
        return d[from][to];
    }

    //最短経路を求める
    vector<ll> get_path(ll from, ll to) {
        if (d[from][to] == 1LL << 60) return {};
        vector<ll> path;
        for(ll at = from; at != to; at = next[at][to]){
            if (at == -1) return {};
            path.push_back(at);
        }
        path.push_back(to);
        return path;
    }

    //到達可能か調べる
    bool cango(ll from, ll to){
        return d[from][to] != 1LL << 60;
    }

    //負の閉路の有無を調べる
    bool closed(){
        return cl;
    }
};

//UnionFind
struct UnionFind{
    vector<ll>par, rank, siz;
    UnionFind(ll n):par(n, -1), rank(n, 0), siz(n, 1){}

    ll root(ll x){
        if(par[x] == -1){
            return x;
        }else{
            return par[x] = root(par[x]);
        }
    }
    //連結判定
    bool issame(ll x, ll y){
        return root(x) == root(y);
    }
    //連結
    bool unite(ll x, ll y){
        ll rx = root(x), ry = root(y);
        if(rx == ry){
            return false;
        }
        if(rank[rx] < rank[ry]){
            swap(rx, ry);
        }
        par[ry] = rx;
        if(rank[rx] == rank[ry]){
            rank[rx]++;
        }
        siz[rx] += siz[ry];
        return true;
    }

    ll size(ll x){
        return siz[root(x)];
    }
};

struct kruskal{
    ll n;
    vector<Edge2> edges;
    //kruskalの構築
    kruskal(Graph &g){
        n = g.size();
        for(ll i = 0; i < n; i++){
            for(auto e : g[i]){
                edges.emplace_back(i, e.to, e.cost);
            }
        }
    }

    //最小全域木のコストを求める
    ll get_mincost(){
        sort(edges.begin(), edges.end());
        UnionFind uf(n);
        ll ret = 0;
        for(auto e : edges){
            if(uf.unite(e.from, e.to))ret += e.cost;
        }
        return ret;
    }

    //最大全域木のコストを求める
    ll get_maxcost(){
        sort(edges.rbegin(), edges.rend());
        UnionFind uf(n);
        ll ret = 0;
        for(auto e : edges){
            if(uf.unite(e.from, e.to))ret += e.cost;
        }
        return ret;
    }
};

//木の直径を求める
ll tree_diameter(Graph g){
    ll n = g.size();
    dijkstra d(g, 0);
    ll mx = 0, idx = -1;
    for(ll i = 0; i < n; i++){
        if(mx < d.get_cost(i)){
            mx = d.get_cost(i);
            idx = i;
        }
    }

    dijkstra d2(g, idx);
    ll mx2 = 0;
    for(ll i = 0; i < n; i++){
        if(mx2 < d2.get_cost(i)){
            mx2 = d2.get_cost(i);
        }
    }

    return mx2;
}

//LCA

struct LCA {
    vector<vector<ll>> parent;  // parent[k][u]:= u の 2^k 先の親
    vector<ll> dist;            // root からの距離

    LCA(Graph &g, ll root = 0){
        vector<vector<Edge3>> G(g.size());
        for(ll i = 0; i < g.size(); i++){
            for(auto e : g[i]){
                G[i].emplace_back(e.to);
            }
        }
        ll V = G.size();
        ll K = 1;
        while ((1 << K) < V) K++;
        parent.assign(K, vector<ll>(V, -1));
        dist.assign(V, -1);
        dfs(G, root, -1, 0);
        for (ll k = 0; k + 1 < K; k++) {
            for (ll v = 0; v < V; v++) {
                if (parent[k][v] < 0) {
                    parent[k + 1][v] = -1;
                } else {
                    parent[k + 1][v] = parent[k][parent[k][v]];
                }
            }
        }
    }

    void dfs(const vector<vector<Edge3>> &G, ll v, ll p, ll d) {
        parent[0][v] = p;
        dist[v] = d;
        for (auto e : G[v]) {
            if (e.to != p) dfs(G, e.to, v, d + 1);
        }
    }

    ll query(ll u, ll v) {
        if (dist[u] < dist[v]) swap(u, v);  // u の方が深いとする
        ll K = parent.size();
        // LCA までの距離を同じにする
        for (ll k = 0; k < K; k++) {
            if ((dist[u] - dist[v]) >> k & 1) {
                u = parent[k][u];
            }
        }
        // 二分探索で LCA を求める
        if (u == v) return u;
        for (ll k = K - 1; k >= 0; k--) {
            if (parent[k][u] != parent[k][v]) {
                u = parent[k][u];
                v = parent[k][v];
            }
        }
        return parent[0][u];
    }

    ll get_dist(ll u, ll v){
        return dist[u] + dist[v] - 2 * dist[query(u, v)];
    }

    bool is_on_path(ll u, ll v, ll a){
        return get_dist(u, a) + get_dist(a, v) == get_dist(u, v);
    }
};

struct AuxiliaryTree {
    vector<vector<ll>> G0;
    LCA &lca;

    AuxiliaryTree(LCA &lca) : lca(lca) {}

    void build(ll k, vector<ll> &vs) {
        sort(vs.begin(), vs.begin() + k, [&](ll a, ll b) { return lca.dist[a] < lca.dist[b]; });
        stack<ll> stk;
        stk.push(vs[0]);
        G0[vs[0]].clear();

        for (ll i = 1; i < k; ++i) {
            ll w = lca.query(vs[i - 1], vs[i]);

            if (w != vs[i - 1]) {
                ll last = stk.top(); stk.pop();
                while (!stk.empty() && lca.dist[w] < lca.dist[stk.top()]) {
                    G0[stk.top()].push_back(last);
                    last = stk.top(); stk.pop();
                }
                if (stk.empty() || stk.top() != w) {
                    stk.push(w);
                    vs.push_back(w);
                    G0[w] = { last };
                } else {
                    G0[w].push_back(last);
                }
            }

            stk.push(vs[i]);
            G0[vs[i]].clear();
        }

        while (stk.size() > 1) {
            ll u = stk.top(); stk.pop();
            G0[stk.top()].push_back(u);
        }
    }
};


//centroid_decomposition
struct centroid_decomposition{
    Graph g;
    ll n;
    vector<ll> size;
    ll centroid;
    centroid_decomposition(Graph f) : g(f){
        g = f;
        n = g.size();
        size.resize(n, 1);
        stack<tuple<ll, ll, ll>> st;
        st.push({0, 0, 0});
        while (!st.empty()) {
            ll v, p, t;
            tie(v, p, t) = st.top();
            st.pop();

            if (t == 0) {
                st.push({v, p, 1});
                for (auto [c, d] : g[v]) {
                    if (c != p) {
                        st.push({c, v, 0});
                    }
                }
            } else {
                bool is_centroid = true;
                for (auto [c, d] : g[v]) {
                    if (c != p) {
                        size[v] += size[c];
                        if (size[c] > n / 2) {
                            is_centroid = false;
                        }
                    }
                }
                if (is_centroid && n - size[v] <= n / 2) {
                    centroid = v;
                }
            }
        }
    }
    
    //木の重心を求める
    ll get_centroid(){
        return centroid;
    }

    //重心によって分解された部分木を求める
    vector<vector<ll>> get_subtree(){
        vector<vector<ll>> comp(n);
        stack<tuple<ll, ll, ll>> st;
        for(auto [v, w] : g[centroid]){
            st.push({v, centroid, v});
        }

        while(!st.empty()){
            auto[v, p, i] = st.top();
            st.pop();
            comp[i].push_back(v);
            for(auto [c, d] : g[v]){
                if(c != p){
                    st.push({c, v, i});
                }
            }
        }

        return comp;
    }
};
//----------------------normal-----------------------//
const ld PI = 3.1415926535897932;

const ll mod = 998244353;
const ll MOD = 1000000007;

const ll dx[] = {-1, 0, 1, 0, -1, 1, 1, -1};
const ll dy[] = {0, 1, 0, -1, 1, 1, -1, -1};

const string ALPHA = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alpha = "abcdefghijklmnopqrstuvwxyz";

//using mint = modint;
//using mint = static_modint<1777777777>;
using mint = modint998244353;
//using mint = modint1000000007;

/*-----------------------function------------------------*/
bool f(string &s){
    string t = s;
    reverse(t.begin(), t.end());
    return s == t;
}
/*------------------------solve--------------------------*/
void solve(){
    ll n; cin >> n;
    ll cnt = 0;
    rep(i,60){
        if(1LL << i & n)cnt++;
    }
    cout << mint(2).pow(cnt).val() - 2 << endl;
}
int main(){
    cin.tie(nullptr);
    cout.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    srand((unsigned)time(NULL));
    //ll T; cin >> T;
    ll T = 1;
    while(T--){
        solve();
    }
    return 0;
}