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 s = S.size(); int t = T.size();
	int ans = 114514;  
	for(int i = 0; i <= s-t; i++){
		int ch = 0; 
		for(int j = 0; j < t; j++){
			if(S.at(i+j) != T.at(j)) ch ++; 
		}
		ans = min(ch, ans); 
	}
	cout << ans << "\n"; 
}