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 n = s.length() ;
	int m = t.length() ;
	int ans = n ;
	for(int i = 0 ; i < n-m+1 ; i++){
	    int cnt = 0 ;
		for(int j = 0 ; j < m ;j++){
			if(t[j] != s[i + j]) cnt++;
		}
	 ans = min(ans , cnt);
	}
	cout << ans ;
}