Given are two strings S and T.

Let us change some of the characters in S so that T will be a substring of S.

At least how many characters do we need to change?

Here, a substring is a consecutive subsequence. For example, `xxx` is a substring of `yxxxy`, but not a substring of `xxyxx`.

Constraints

* The lengths of S and T are each at least 1 and at most 1000.
* The length of T is at most that of S.
* S and T consist of lowercase English letters.

Input

Input is given from Standard Input in the following format:


S
T


Output

Print the minimum number of characters in S that need to be changed.

Examples

Input

cabacc
abc


Output

1


Input

codeforces
atcoder


Output

6
#include<bits/stdc++.h>
using namespace std;
const int N=1011;
char s[N],t[N];
int n,m;
int main(){
	cin>>s>>t;
	n=strlen(s);
	m=strlen(t);
	int i,j,ans=m;
	for(i=0;i+m<n+1;++i){
		int u=0;
		for(j=0;j<m;++j)
			u+=t[j]!=s[i+j];
		ans=min(ans,u);
	}
	cout<<ans<<endl;
}
