inline int read()

{

    int ans=;

    char last=' ',ch=getchar();

    while(ch<''||ch>'') last=ch,ch=getchar();

    while(ch>=''&&ch<='') ans=ans*+ch-'',ch=getchar();

    if(last=='-') ans=-ans;

    return ans;

}

inline char read()

{

    char c;

    do

    {

        c=getchar();

    }while(c==' '||c=='\n'||c=='\0'||c=='\t');

}

#include<iostream>

#include<algorithm>

#include<cstdio>

#include<cstring>

#include<cmath>

#include<cstdlib>

using namespace std;

typedef long long ll;

typedef long double ld;

typedef pair<int,int> pr;

const double pi=acos(-);

#define rep(i,a,n) for(int i=a;i<=n;i++)

#define per(i,n,a) for(int i=n;i>=a;i--)

#define Rep(i,u) for(int i=head[u];i;i=Next[i])

#define clr(a) memset(a,0,sizeof a)

#define pb push_back

#define mp make_pair

#define fi first

#define sc second

ld eps=1e-;

ll pp=;

ll mo(ll a,ll pp)                //取模运算
{
    if(a>= && a<pp)return a;
    a%=pp;
    if(a<)a+=pp;
    return a;
}

ll powmod(ll a,ll b,ll pp)     //a^b%p=
{
    ll ans=;
    for(;b;b>>=,a=mo(a*a,pp))
    if(b&)ans=mo(ans*a,pp);
    return ans;
}

ll read()             //快读
{

    ll ans=;

    char last=' ',ch=getchar();

    while(ch<'' || ch>'')last=ch,ch=getchar();

    while(ch>='' && ch<='')ans=ans*+ch-'',ch=getchar();

    if(last=='-')ans=-ans;

    return ans;

}