#include<bits/stdc++.h>
using namespace std;
#define IOS ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
#define int long long
#define inf 0x3f3f3f3f
#define mod1 1000000007
#define mod2 998244353
#define f first
#define s second
#define pb push_back
#define eb emplace_back
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define rep(i,a,b) for(int i=a;i>=b;i--)
#define m1(a,b) memset(a,b,sizeof a)
#define m2(a,b) memcpy(a,b,sizeof b)
using ld = long double;
using str = string;
using pi = pair<int,int>;
using pd = pair<ld,ld>;
using vi = vector<int>;
using vb = vector<bool>;
using vd = vector<ld>; 
using vs = vector<str>;
using vpi = vector<pi>;
using vpd = vector<pd>;
const ld PI = acos((ld)-1);
const int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};
template<class T> using pqg = priority_queue<T,vector<T>,greater<T>>;
template<typename T, typename U> void umin(T& a, U b){if (a > b) a = b;}
template<typename T, typename U> void umax(T& a, U b){if (a < b) a = b;}
namespace IO{
    inline int r()
    {
        int X=0; bool flag=1; char ch=getchar();
        while(ch<'0'||ch>'9') {if(ch=='-') flag=0; ch=getchar();}
        while(ch>='0'&&ch<='9') {X=(X<<1)+(X<<3)+ch-'0'; ch=getchar();}
        if(flag) return X;
        return ~(X-1);
    }
    inline void w(int X)
    {
        if(X<0) {X=~(X-1); putchar('-');}
        if(X>9) write(X/10);
        putchar(X%10+'0');
    }
}
namespace math{
    int qmi(int a, int k, int p)
    {
        int res = 1 % p;
        while (k)
        {
            if (k & 1) res = res * a % p;
            a = a * a % p;
            k >>= 1;
        }
        return res;
    }
    bool is_prime(int x)  
    {
        if (x < 2) return false;
        for (int i = 2; i <= x / i; i ++ )
            if (x % i == 0)
                return false;
        return true;
    }
}
signed main(){

    return 0;
}