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

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