/*#include <bits/stdc++.h>
using namespace std;
int segment[200001], A[50001], B[50001], pos[100001], n, con[50001];
int sum(int node, int start, int End, int l, int r)
{
if(l<=start&&r>=End)return segment[node];
if(start>r||End<l)return 0;
int mid=(start+End)/2;
return sum(node*2, start, mid, l, r)+sum(node*2+1, mid+1, End, l, r);
}
void update(int node, int start, int End, int target)
{
if(start==End)
{
if(start==target)segment[node]++;
return ;
}
if(start<=target&&End>=target)
{
segment[node]++;
}
else
{
return ;
}
int mid=(start+End)/2;
update(node*2, start, mid, target);
update(node*2+1, mid+1, End, target);
}
int main()
{
scanf("%d", &n);
for(int i=1;i<=n;i++)scanf("%d", &A[i]);
for(int i=1;i<=n;i++)
{
scanf("%d", &B[i]);
pos[B[i]]=i;
}
int ans=0, m, k, p;
for(int i=1;i<=n;i++)
{
p=pos[A[i]];
ans+=sum(1, 1, n, p, n);
con[p]=1;
update(1, 1, n, p);
}
printf("%d", ans);
}
*/
/*
#include <bits/stdc++.h>
using namespace std;
int main()
{
int t, n, arr[100001], m, check[100001], canuse[100001], top;
scanf("%d", &t);
bool ans;
while(t--)
{
m=2147483647;
top=0;
memset(check, 0, sizeof(check));
scanf("%d", &n);
for(int i=1; i<=n; i++)
{
scanf("%d", &arr[i]);
m=min(m, arr[i]);
}
for(int i=1; i<=n; i++)
{
if(arr[i]%m==0)
{
top++;
canuse[top]=arr[i];
}
else
{
check[i]=1;
}
}
sort(canuse+1, canuse+1+top);
top=0;
for(int i=1; i<=n; i++)
{
if(check[i]==1)
continue;
top++;
arr[i]=canuse[top];
}
ans=true;
for(int i=2; i<=n; i++)
{
if(arr[i]>=arr[i-1])
{
continue;
}
else
{
ans=false;
break;
}
}
if(ans)
{
printf("YES\n");
}
else
{
printf("NO\n");
}
}
}*/
/*
#include <bits/stdc++.h>
using namespace std;
int Gcd(int x, int y)
{
if(x==0)return y;
return Gcd(y%x, x);
}
int main()
{
string s;
int ha=1, haha=0, hahaha;
cin >> s;
for(int i=0;i<s.size();i++)
{
if(s[i]=='.')
{
hahaha=i+1;
break;
}
}
for(int i=1;i<=s.size()-hahaha;i++)
{
ha*=10;
}
for(int i=hahaha;i<s.size();i++)
{
haha*=10;
haha+=s[i]-'0';
}
int gcd=Gcd(haha, ha);
printf("%d %d", haha/gcd, ha/gcd);
}*/
/*
#include <bits/stdc++.h>
using namespace std;
int main()
{
int dp[100001][2]={};
dp[1][1]=1;
dp[1][0]=1;
for(int i=2;i<=100000;i++)
{
dp[i][1]=dp[i-1][1]+dp[i-1][0];
dp[i][0]=dp[i-1][1];
dp[i][1]%=1000000007;
dp[i][0]%=1000000007;
}
int n;
scanf("%d", &n);
printf("%d", (dp[n][1]+dp[n][0])%1000000007);
}*/
/*
#include <bits/stdc++.h>
using namespace std;
int main()
{
int k, n;
cin >> k >> n;
printf("%d", k*n);
}*/
/*
#include <bits/stdc++.h>
using namespace std;
int gcd(int x, int y)
{
if(y==0)return x;
return gcd(y, x%y);
}
int main()
{
int a, b, temp;
scanf("%d %d", &a, &b);
if(a<b)
{
temp=a;
a=b;
b=temp;
}
int ha=gcd(a, b);
if(ha==1)
{
printf("coprime");
return 0;
}
printf("no");
}
*/
/*
#include <bits/stdc++.h>
using namespace std;
int main()
{
int n, arr[100001];
scanf("%d", &n);
for(int i=1; i<=n; i++)
scanf("%d", &arr[i]);
sort(arr+1, arr+1+n);
int mid=(n+1)/2, top=0, haha[100001];
long long int need[100001]= {};
for(int i=mid; i<=n; i++)
{
top++;
haha[top]=arr[i];
}
//printf("\ntop:%d\n", top);
for(int i=2; i<=top; i++)
{
need[i]=need[i-1]+(haha[i]-haha[i-1])*(i-1);
}
//printf("\nneed:%d\n", need[2]);
int t, x, start, End;
scanf("%d", &t);
while(t--)
{
scanf("%d", &x);
if(x>=need[top])
{
printf("%d\n", haha[top]+(x-need[top])/top);
}
else
{
start=1, End=top;
while(start<End)
{
mid=(start+End)/2;
if(need[mid]>x)
{
End=mid-1;
}
else if(need[mid]<x)
{
start=mid;
if(start+1==End)
{
if(need[start+1]<=x)
start++;
break;
}
}
else
{
start=mid;
break;
}
}
//printf("arr:%d\n", haha[start]);
printf("%d\n", haha[start]+(x-need[start])/(start));
}
}
}*/