/*
███╗ ███╗ █████╗ ██████╗ ███████╗ ██████╗ ██╗ ██╗ ███╗ ███╗ █████╗ ██████╗ ██████╗██╗ ██╗███████╗██╗ ██╗ ██╗ ██╗██╗██╗
████╗ ████║██╔══██╗██╔══██╗██╔════╝ ██╔══██╗╚██╗ ██╔╝██╗ ████╗ ████║██╔══██╗██╔══██╗██╔════╝██║ ██║██╔════╝██║ ██║ ██║ ██║██║██║
██╔████╔██║███████║██║ ██║█████╗ ██████╔╝ ╚████╔╝ ╚═╝ ██╔████╔██║███████║██████╔╝██║ ███████║█████╗ ██║ ██║ ███████║██║██║
██║╚██╔╝██║██╔══██║██║ ██║██╔══╝ ██╔══██╗ ╚██╔╝ ██╗ ██║╚██╔╝██║██╔══██║██╔══██╗██║ ██╔══██║██╔══╝ ██║ ██║ ██╔══██║██║██║
██║ ╚═╝ ██║██║ ██║██████╔╝███████╗ ██████╔╝ ██║ ╚═╝ ██║ ╚═╝ ██║██║ ██║██║ ██║╚██████╗██║ ██║███████╗███████╗███████╗█████╗██║ ██║██║██║
╚═╝ ╚═╝╚═╝ ╚═╝╚═════╝ ╚══════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝╚═╝ ╚═╝╚═╝ ╚═╝ ╚═════╝╚═╝ ╚═╝╚══════╝╚══════╝╚══════╝╚════╝╚═╝ ╚═╝╚═╝╚═╝
*/
/*
ඞ
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠉⠉⠉⠉⠉⠻⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀ ⣠⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀ ⣿⣿⣯⠁⠀⠀⠀⠀⠀ ⠙⢿⣷⡄
⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀ ⣿⣿⣿ ⣿⣷
⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀ ⣿⣿⣿⣷⣦⣀⣀⣀⣀⣀⣀⣀⣿⣿
⢸⣿⡇ ⣿⣿⡇⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⡇ ⣿⣿⡇⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⡿⢻⡇
⠀⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇
⠀⣿⣿⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇
⠀⣿⣿⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇
⠀⢿⣿ ⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇
⠀⠸⣿⣦⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿
⠀⠀⠛⢿⣿⣿⣿⣿⡇ ⠀⣠⣿⣿⣿⣿⣄ ⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡆ ⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀ ⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿ ⠀⠈⠻⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁
*/
#include<bits/stdc++.h>
#define ll long long
#define pii pair<int, int>
#define pll pair<ll, ll>
#define plll pair<pll, pll>
#define pdd pair<double, double>
#define pu push_back
#define po pop_back
#define fi first
#define se second
#define fifi fi.fi
#define fise fi.se
#define sefi se.fi
#define sese se.se
#define cekcek cout<<'c'<<'e'<<'k'<<endl
using namespace std;
int main(){
ios_base::sync_with_stdio(0); cin.tie(NULL); cout.tie(NULL);
}
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