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;

int main()
{
	string S,T;
	cin>>S>>T;
	int l1=S.length();
	int l2=T.length();
	int l=l1-l2+1;
	int Max=0;
	for(int i=0;i<l;i++)
	{
		int sum=0;
		for(int j=0;j<l2;j++)
			if(S[i+j]==T[j]) ++sum;
		Max=max(Max,sum);
	}
	printf("%d",l2-Max);
	return 0;
}
