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
import java.util.*;
class Main{
public static void main(String[]args){
Scanner sc=new Scanner(System.in);
char[] s=sc.next().toCharArray();
  char[] t=sc.next().toCharArray();
  int min=1000000;
  for(int i=0;i<s.length-t.length+1;i++){
    int a=0;
    for(int j=0;j<t.length;j++){
    	if(s[i+j]==t[j])a++;
    }
    min=Math.min(min,t.length-a);
  }System.out.println(min);
}
}