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 a,b;int gb,ans;
	cin>>a>>b;
	int la=a.size(),lb=b.size();
	ans=la;
	for(int i=0;i<=la-lb;i++)
	{
		gb=0;
		for(int j=i;j<i+lb;j++)
		{
			if(a[j]!=b[j-i]) gb++;
		}
		ans=min(ans,gb);
	}
	cout<<ans;
	return 0;
}