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;
	cin>>t;
	int ans=0,sum;
	for(int i=0;i<=s.length()-t.length();i++){
		sum=0;
		for(int j=0;j<t.length();j++){
			if(s[i+j]==t[j])
			sum++;
		}
		ans=max(ans,sum);
	}
	cout<<t.length()-ans<<endl;
}