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 cnt=0,lt=t.length(),ls=s.length();
	int m=1001;
	int sub=ls-lt;
	for (int i=0;i<=sub;i++)
	{
		for (int j=0;j<lt;j++)
		{
			if (s[i+j]!=t[j])
				cnt++;
		}
		m=min(m,cnt);
		cnt=0;
	}
	cout<<m;
} 