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 ans = T.length();
	for(int i=0; i<S.length()-T.length()+1; ++i){
		int cnt = 0;
		for(int j=0; j<T.length(); ++j){
			if(T[j]!=S[j+i]) ++cnt;
		}
		ans = min(ans,cnt);
	}
	cout << ans << endl;
	return 0;
}