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 ans = 0;
	for (int i = 0; i <= (S.size() - T.size()); i++)
	{
		int cnt = 0;
		for (int j = 0; j < T.size(); j++)
		{
			if (S.at(i + j) == T.at(j))cnt++;
		}
		ans = max(cnt, ans);
	}
	cout << T.size() - ans << endl;
}