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;
string a,b;
int ans=INT_MAX;
int main(){
	cin>>a>>b;
	for(int i=0;i<a.length()-b.length()+1;i++){
		int cnt=0;
	    for(int j=i;j<i+b.length();j++)cnt+=a[j]!=b[j-i];
	    ans=min(ans,cnt);
	}
	cout<<ans<<endl;
}
