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> 
#define PB push_back
using namespace std;

int main(){
	string a,t;
	cin>>a>>t;
	int f=t.length();
	for(int i=0;i<(a.length()-t.length())+1;i++){
		int k=t.length();
		for(int j=0;j<t.length();j++){
			a[j+i]==t[j]?k--:i=i;
		}
		f=min(f,k);
	}
	cout<<f<<endl;
}
