// clang-format off
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>

#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2")

using namespace std;
using namespace __gnu_pbds;

typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> pii;
typedef vector<ll> d1;
typedef vector<d1> d2;
typedef vector<pii> d1p;
typedef vector<d1p> d2p;
typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

ostream& operator<<(ostream&cout, const pii&a){cout<<a.first<<","<<a.second;return cout;}
pii min(const pii &a, const pii &b){if(a.first<b.first) return a;else return b;}
pii max(const pii &a, const pii &b){if(a.first>b.first) return a;else return b;}
template<typename T> T min(vector<T> &a){return *min_element(a.begin(), a.end());}
template<typename T> T max(vector<T> &a){return *max_element(a.begin(), a.end());}
template<typename T> T sum(vector<T>&a){T m=0;for(T&i:a)m+=i;return m;}
template<typename T> void print(vector<T>&a){for(T&i:a)cout<<i<<" ";cout<<"\n";}
template<typename T> void print(vector<vector<T>>&a){for(vector<T>&i:a)print(i);}

#define stuff ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
#define fori(x, n) for(ll i = x; i < n; ++i)
#define forj(x, n) for(ll j = x; j < n; ++j)
#define fork(x, n) for(ll k = x; k < n; ++k)
#define foru(p, t) for(ll i = p; i < t.size(); i+=i&-i)
#define ford(r, t) for(ll i = r; i > 0; i-=i&-i)
#define all(a) a.begin(), a.end()
#define sort(a) sort(all(a))
#define reverse(a) reverse(all(a))
#define unique(a) a.erase(unique(all(a)), a.end());
#define wt ll _t; cin>>_t; while(_t--)
#define __lg(x) 63ll - __builtin_clzll(x)
#define pb push_back
#define pob pop_back
#define endl "\n"
#define F first
#define S second
#define B back()

signed main(){
	
}