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 <iostream>
using namespace std;

int main()
{
	string a, b;
	cin >> a >> b;
	int n = a.size(), m = b.size(), ans = 0x7fffffff;
	for (int i = 0; i <= n - m; ++i)
	{
		int s = 0;
		for (int j = 0; j < m; ++j)
			if (a[j + i] != b[j])
				++s;
		ans = ans < s ? ans : s;
	}
	cout << ans;
	return 0;
}