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()
{
	int i,j,n,s=10000000,m=10000000;
	string a,b;
	cin>>a>>b;
	for(i=0;i<a.size()-b.size()+1;i++)
	{
		s=0;
		for(j=0;j<b.size();j++)
			if(a[i+j]!=b[j]) s++;
		m=min(s,m);
	}
	cout<<m;
}