头文件

#include<bits/stdc++.h>
// #include<iostream>
// #include<stdio.h>
// #include<iomanip>
// #include<stack>
// #include<queue>
// #include<algorithm>
// #include<cstring>
// #include<map>
// #include<vector>
// #include<numeric>
// #include<iterator>
// #include<cmath>
#define met(a,x) memset(a,x,sizeof(a));
#define rep(i,a,b) for(int i = a;i <= b;i++)
#define bep(i,a,b) for(int i = a;i >= b;i--)
#define lowbit(x) (x&(-x))
#define mid ((l + r) >> 1)
#define len (r - l + 1)
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define pb push_back
using namespace std;
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a%b); }
int lcm(int a, int b) { return a * b / gcd(a, b); }
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int>Pi;
typedef pair<int,pair<int,int> > Pii;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const double PI = acos(-1);

const int maxn = 100010;
const int mod=1000000007;
ll a[maxn];


int read(){
    int flag=1;
    int sum=0;
    char c=getchar();
    while(c<'0'||c>'9'){
        if(c=='-')flag=-1;
        c=getchar();
    }
    while(c>='0'&&c<='9'){
        sum=sum*10+c-'0';
        c=getchar();
    }
    return sum*flag;
}
ll Read(){
    int flag=1;
    ll sum=0;
    char c=getchar();
    while(c<'0'||c>'9'){
        if(c=='-')flag=-1;
        c=getchar();
    }
    while(c>='0'&&c<='9'){
        sum=sum*10+c-'0';
        c=getchar();
    }
    return sum*flag;
}
ll quickmul(ll a,ll b){
    ll ans=0;
    while(b){
        if(b&1){
            ans=(ans+a)%mod;
        }
        a=(a+a)%mod;
        b>>=1;
    }
    return ans;
}
ll quickpow(ll a,ll b){
    ll ans=1;
    while(b){
        if(b&1)
            ans=(ans*a)%mod;
        a=(a*a)%mod;
        b>>=1;
    }
    return ans;
}
int main()
{
    
    return 0;
}
 

 

#include<map>
#include<set>
#include<cmath>
#include<deque>
#include<queue>
#include<stack>
#include<string>
#include<bitset>
#include<cstdio>
#include<vector>
#include<iomanip>
#include<cstring>
#include<sstream>
#include<iostream>
#include<algorithm>
#include<unordered_map>
//#include<bits/stdc++.h>
#define fi first
#define se second
#define eps 1e-8
#define ll long long
#define ull unsigned long long
#define pb push_back
#define inf 0x3f3f3f3f
#define INF 0x3f3f3f3f3f3f3f3f
#define P pair<ll, ll>
#define pi acos(-1)
#define lson l,mid,rt*2
#define rson mid+1,r,rt*2+1
#define lowbit(x) (x&(-x))
#define SZ(x) ((ll)(x).size())
#define met(a,x) memset(a,x,sizeof(a))
#define openin(x) freopen(x, "r", stdin)
#define openout(x) freopen(x, "w",stdout)
#define rep(i,a,b) for(int i = a;i <= b;i++)
#define bep(i,a,b) for(int i = a;i >= b;i--)
#define ios() ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
using namespace std;
ll mod = 998244353;
ll gcd(ll a, ll b) { return b == 0 ? a : gcd(b, a % b); }
ll lcm(ll a, ll b) { return a * b / gcd(a, b); }
int days[15] = { 0,31,28,31,30,31,30,31,31,30,31,30,31 };
int is_leapyear(int y) {return y % 400 == 0 || (y % 4 == 0 && y % 100 != 0);}
int dx[8] = {0,0,1,-1,-1,-1,1,1};
int dy[8] = {1,-1,0,0,-1,1,-1,1};
inline ll read() {
    ll x = 0, sign = 1; char ch = getchar();
    for (; !isdigit(ch); ch = getchar()) if (ch == '-') sign = -1;
    for (; isdigit(ch); ch = getchar()) x = x * 10 + ch - '0';
    return sign * x;
}
inline void write(ll x){
    char r[30];
    int t = 0;
    if(x < 0){
        x = -x;
        putchar('-');
    }
    do{
        r[t++] = x % 10 + '0';
        x /= 10;
    }while(x);
    while(t)putchar(r[--t]);
}
inline void writesp(ll x){write(x);putchar(' ');}
inline void writeln(ll x){write(x);putchar('\n');}
ll qpow(ll a, ll b) {
    ll ans = 1;
    while (b) {
        if (b & 1)ans = ans * a % mod;
        a = a * a % mod;
        b >>= 1;
    }
    return ans;
}
int main(){

    return 0;
}