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;
char a[1005],b[1005];
int main()
{
	cin>>(a+1)>>(b+1);
	int n=strlen(a+1),m=strlen(b+1);
	int ans=2147483647;
	for(int i=1;i+m-1<=n;++i)
	{
		int tmp=0;
		for(int j=1;j<=m;++j)if(b[j]!=a[i+j-1])++tmp;
		ans=min(ans,tmp);
	}
	printf("%d\n",ans);
	return 0;
}