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 maxn=1e3+5;
char s[maxn],t[maxn];
int main()
{
	scanf("%s%s",s,t);
	int lens=strlen(s),lent=strlen(t),ans=0;
	for(int i=0;i+lent<=lens;i++)
	{
		int cnt=0;
		for(int j=0;j<lent;j++)
			cnt+=(s[i+j]==t[j]);
		ans=max(ans,cnt);
	}
	printf("%d\n",lent-ans);
}	