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;
string S,T;
int main()
{
	cin>>S>>T;
	int ans=T.size();
	for(int i=0;i+T.size()<=S.size();i++)
	{
		int c=0;
		for(int j=0;j<T.size();j++)c+=S[i+j]!=T[j];
		if(ans>c)ans=c;
	}
	cout<<ans<<endl;
}