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 , c = 0;

	for(int i = 0 ;i <= s.size()-t.size();i++)
	{
		for(int j = 0;j < t.size();j++)
			if(s[i + j] == t[j])
				cnt++;

	c = max(c,cnt);
	cnt = 0;
	}
	cout << t.size() - c;
}