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 s,t;
int sl,tl;
int main(){
	cin>>s>>t;
	sl = s.length();
	tl = t.length();
	int ans = 1946081700;
	for(int i=0;i+tl<=sl;i++){
		int tm = 0;
		for(int j = 0;j<tl;j++){
			if(s[i+j]!=t[j]) tm++;
		}
		ans = min(tm,ans);
	}
	cout<<ans;
} 