/*
	Author: Sean_xzx
	Right Output! & Accepted!
本题核心：
1.
本题步骤：
1.
*/
#include <bits/stdc++.h>

#define fz(i, a, b) for(int i = a; i <= b; i++)
#define fr(i, a, b) for(int i = a; i >= b; i--)
#define ufz(i, a, b) for(int i = a; i < b; i++)
#define ufr(i, a, b) for(int i = a; i > b; i--)
#define rp(i, a) for(int i = 1; i <= a; i++)
#define pr(i, a) for(int i = a; i >= 1; i--)
#define urp(i, a) for(int i = 0; i < a; i++)
#define upr(i, a) for(int i = a; i > 0; i--)
#define go(i, a) for(auto i : a)

//#define int long long
#define LL long long
#define ULL unsigned long long
#define PII pair<int, int>
#define PLL pair<long long, long long>
#define fi first
#define se second
const double eps15 = 1e-15, eps8 = 1e-8;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}, inf = 0x7fffffff, inf_ = 0x80000000;//, inf3f = 0x3f3f3f3f;
const LL INF = 0x7fffffffffffffff, INF_ = 0x8000000000000000;
//const int mod = 1e9 + 7;
//const int mod = 998244353;
int gcd(int a, int b){ return b ? a : gcd(b, a % b);}
int lcm(int a, int b){ return a / gcd(a, b) * b;}

template <typename T> inline void rd(T &x){
	x = 0; bool f = true; char ch = getchar();
	while(ch < '0' || ch > '9'){ f = ch == '-' ? false : true; ch = getchar();}
	while(ch >= '0' && ch <= '9'){ x = (x << 1) + (x << 3) + (ch ^ '0'); ch = getchar();}
	if(!f) x = -x;
}
template <typename T, typename ...Args> inline void rd(T &x, Args &...args){ rd(x); rd(args...);}
/***********************************************code under the there********************************************/
using namespace std;

int main(){
	/*
	freopen(".in", "r", stdio);
	freopen(".out", "w", stdout);
	*/
	return 0;
}