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/*************************************************************************
SPDX-License-Identifier: MIT
Copyright (c) 2025 Qazi Fahim Farhan (@fahimfarhan)
May the CodeForces be with you!
************************************************************************/
/**
// ⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣶⣶ ⠄⠄⠄⠄⠄⠄⢴⡶⣶⣶⣶⡒⣶⣶⣖⠢⡄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
// ⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣶⣶ ⠄⠄⠄⠄⠄⠄⢠⣿⣋⣿⣿⣉⣿⣿⣯⣧⡰⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
// ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⣿⣿⣹⣿⣿⣏⣿⣿⡗⣿⣿⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
// ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣾⣿⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠟⡛⣉⣭⣭⣭⠌⠛⡻⢿⣿⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
// ⣿⣿⣿⣿⣿⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⣤⡌⣿⣷⣯⣭⣿⡆⣈⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
// ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⠄⠄⠄⠄⠄⠄⠄⢻⣿⣿⣿⣿⣿⣿⣿⣷⢛⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
// ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⢻⣷⣽⣿⣿⣿⢿⠃⣼⣧⣀⠄⠄⠄⠄⠄⠄⠄⠄⠄
// ⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣛⣻⣿⠟⣀⡜⣻⢿⣿⣿⣶⣤⡀⠄⠄⠄⠄⠄
// ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⢠⣤⣀⣨⣥⣾⢟⣧⣿⠸⣿⣿⣿⣿⣿⣤⡀⠄⠄⠄
// ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⢟⣫⣯⡻⣋⣵⣟⡼⣛⠴⣫⣭⣽⣿⣷⣭⡻⣦⡀⠄
// ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⢰⣿⣿⣿⢏⣽⣿⢋⣾⡟⢺⣿⣿⣿⣿⣿⣿⣷⢹⣷⠄
// ⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⣿⣿⣿⢣⣿⣿⣿⢸⣿⡇⣾⣿⠏⠉⣿⣿⣿⡇⣿⣿⡆
// ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⣿⣿⣿⢸⣿⣿⣿⠸⣿⡇⣿⣿⡆⣼⣿⣿⣿⡇⣿⣿⡇
// ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⠇⢀⠄⠄⠄⠄⠄⠘⣿⣿⡘⣿⣿⣷⢀⣿⣷⣿⣿⡿⠿⢿⣿⣿⡇⣩⣿⡇
// ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⠃⠄⠄⠄⠄⠄⠄⢻⣷⠙⠛⠋⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡇⣿⣿⡇
*/
#include <bits/stdc++.h>
using namespace std;
#include <bits/stdc++.h>
using namespace std;
#define si(x) scanf("%d",&x)
#define sf(x) scanf("%f",&x)
#define pi(x) printf("%d\n",x)
#define pf(x) printf("%.4f\n",x)
#define ll long long int
#define sll(x) scanf("%I64d",&x);
#define pll(x) printf("%-I64d\n",x);
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
return 0;
}
/* When Panda is Life !
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,a8^ ,d8888' ^Y8888888P'
a88' ,d8888P' I88P"^
,d88' d88888P' "b,
,d88' d888888' `b,
,d88' d888888I `b,
d88I ,8888888' ___ `b,
,888' d8888888 ,d88888b, ____ `b,
d888 ,8888888I d88888888b, ,d8888b, `b
,8888 I8888888I d8888888888I ,88888888b 8,
I8888 88888888b d88888888888' 8888888888b 8I
d8886 888888888 Y888888888P' Y8888888888, ,8b
88888b I88888888b `Y8888888^ `Y888888888I d88,
Y88888b `888888888b, `""""^ `Y8888888P' d888I
`888888b 88888888888b, `Y8888P^ d88888
Y888888b ,8888888888888ba,_ _______ `""^ ,d888888
I8888888b, ,888888888888888888ba,_ d88888888b ,ad8888888I
`888888888b, I8888888888888888888888b, ^"Y888P"^ ____.,ad88888888888I
88888888888b,`888888888888888888888888b, "" ad888888888888888888888'
8888888888888698888888888888888888888888b_,ad88ba,_,d88888888888888888888888
88888888888888888888888888888888888888888b,`"""^ d8888888888888888888888888I
8888888888888888888888888888888888888888888baaad888888888888888888888888888'
Y8888888888888888888888888888888888888888888888888888888888888888888888888P
I888888888888888888888888888888888888888888888P^ ^Y8888888888888888888888'
`Y88888888888888888P88888888888888888888888888' ^88888888888888888888I
`Y8888888888888888 `8888888888888888888888888 8888888888888888888P'
`Y888888888888888 `888888888888888888888888, ,888888888888888888P'
`Y88888888888888b `88888888888888888888888I I888888888888888888'
"Y8888888888888b `8888888888888888888888I I88888888888888888'
"Y88888888888P `888888888888888888888b d8888888888888888'
^""""""""^ `Y88888888888888888888, 888888888888888P'
"8888888888888888888b, Y888888888888P^
`Y888888888888888888b `Y8888888P"^
"Y8888888888888888P `""""^
`"YY88888888888P'
^""""""""'
*/
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