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(){
int t=0,s=0;;
string S,T;
cin >> S>>T;
for(int i=0; i<S.length()-T.length()+1; i++){
	t=0;
	for(int j=0; j<T.length(); j++){
		if(S.at(i+j)==T.at(j)) t++;
		if(s<t) s=t;
	}
}
cout << T.length()-s << endl;

}