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 NOI=0x3f3f3f3f;
int ans=NOI;
string s,t;
int ls,lt,sum,i,j;
int main(){
	cin>>s>>t;
	ls=s.size();
	lt=t.size();
	for(i=0;i<=ls-lt;i++){
	    sum=0;
		for(j=0;j<lt;j++)if(s[i+j]!=t[j])sum++;
		ans=min(ans,sum);
	}
	cout<<ans<<'\n';
	return 0;
}