#include<bits/stdc++.h>
using namespace std;
namespace my_std{
#define ll long long
#define bl bool
ll my_pow(ll a,ll b,ll mod){
ll res=1;
if(!b) return 1;
while(b){
if(b&1) res=(res*a)%mod;
a=(a*a)%mod;
b>>=1;
}
return res;
}
ll qpow(ll a,ll b){
ll res=1;
if(!b) return 1;
while(b){
if(b&1) res*=a;
a*=a;
b>>=1;
}
return res;
}
#define db double
#define pf printf
#define pc putchar
#define fr(i,x,y) for(register ll i=(x);i<=(y);i++)
#define pfr(i,x,y) for(register ll i=(x);i>=(y);i--)
#define go(u) for(ll i=head[u];i;i=e[i].nxt)
#define enter pc('\n')
#define space pc(' ')
#define fir first
#define sec second
#define MP make_pair
#define il inline
#define inf 8e18
#define random(x) rand()*rand()%(x)
#define inv(a,mod) my_pow((a),(mod-2),(mod))
il ll read(){
ll sum=0,f=1;
char ch=0;
while(!isdigit(ch)){
if(ch=='-') f=-1;
ch=getchar();
}
while(isdigit(ch)){
sum=sum*10+(ch^48);
ch=getchar();
}
return sum*f;
}
il void write(ll x){
if(x<0){
x=-x;
pc('-');
}
if(x>9) write(x/10);
pc(x%10+'0');
}
il void writeln(ll x){
write(x);
enter;
}
il void writesp(ll x){
write(x);
space;
}
}
using namespace my_std;