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 q = s.size(), r = t.size();
	int ans = 1001;
	for(int i = 0; i <= q-r; ++i){
		int t1 = 0;
		for(int j = i; j < i + r; ++j){
			if(s[j] != t[j-i]) ++t1;
		}
		ans = min(ans, t1);
	}
	cout << ans;
}