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<iostream> 
using namespace std;
int main(){
	int maxx=0;
	string t,s;
	cin>>t>>s;
	for(int i=0;i<t.length()-s.length()+1;i++){
		int sum=0;
		for(int j=i;j<i+s.length();j++){
			if(s[j-i]==t[j])sum++;
		}
		maxx=max(maxx,sum);
	}
	cout<<s.length()-maxx<<'\n';
}