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 s, t;
	cin >> s >> t;

	int ans = 0;
	int cnt = 0;
	for (int i = 0; i < s.size() - t.size() + 1; ++i) {
		for (int j = 0; j < t.size(); ++j) {
			if (s[i + j] == t[j]) ++cnt;
		}
		ans = max(ans, cnt);
		cnt = 0;
	}

	cout << t.size() - ans << endl;
}