#pragma GCC optimize ("-O3")

#include<bits/stdc++.h>

using namespace std;

typedef long long int ll;

typedef long double ld;

typedef pair<int,int> p32;

typedef pair<ll,ll> p64;

typedef pair<double,double> pdd;

typedef vector<ll> v64;

typedef vector<int> v32;

typedef vector<vector<int> > vv32;

typedef vector<vector<ll> > vv64;

typedef vector<p64> vp64;

typedef vector<p32> vp32;

ll MOD = 998244353;

ll NUM = 1e9+7;

#define forn(i,e) for(ll i = 0; i < e; i++)

#define forsn(i,s,e) for(ll i = s; i < e; i++)

#define rforn(i,s) for(ll i = s; i >= 0; i--)

#define rforsn(i,s,e) for(ll i = s; i >= e; i--)

#define ln "\n"

#define dbg(x) cout<<#x<<" = "<<x<<ln

#define mp make_pair

#define pb push_back

#define ff first

#define ss second

#define INF 1e18

#define fast_cin() ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL)

#define all(x) (x).begin(), (x).end()

#define sz(x) ((ll)(x).size())

#define zer ll(0)

int main() {

}