#line 2 "template.hpp"
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using pl = pair<ll, ll>;
using vl = vector<ll>;
#define rep(i, n) for(ll i = 0; i < (ll)n; i++)
#define rep3(i, l, r) for(ll i = l; i < (ll)r; i++)
#define per(i, n) for(ll i = (ll)n-1; i >= 0; i--)
#define per3(i, l, r) for(ll i = (ll)r-1; i >= (ll)l; i--)
#define all(v) begin(v), end(v)
template<class T, class U> inline void cmax(T& a, U b) { if (a < b) a = b; }
template<class T, class U> inline void cmin(T& a, U b) { if (a > b) a = b; }

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr); ios::sync_with_stdio(false);
    cout << fixed << setprecision(15); cerr << fixed << setprecision(15);
  }
} io_setup;

constexpr char el = '\n';
template<class T, class U> ostream &operator<<(ostream &os, const pair<T, U>& p) { os << p.first << " " << p.second; return os; }
template<class T, class U> istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; }
template<class T> ostream &operator<<(ostream &os, const vector< T > &v) { rep(i, v.size()) os << v[i] << (i + 1 != v.size() ? " " : ""); return os; }
template<class T> istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; }
