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 c=T.size(),t=T.size(),s=S.size();
	for(int i=0;i<s-t+1;i++){
		int q=0;
		for(int j=0;j<t;j++){
			if(T[j]==S[j+i]){
				q++;
			}
		}
		if(c>t-q){
			c=t-q;
		}
	}
	cout<<c;
}
