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.ArrayDeque;
import java.util.Arrays;
import java.util.Scanner;
import java.util.Deque;
public class Main {

    public static void main(String[] args) {
        // write your code here

        Scanner scan = new Scanner(System.in);
String S=scan.next();
        String T=scan.next();
int M=0;
        for(int i=0;i<S.length()-T.length()+1;i++){
            String J=S.substring(i,i+T.length());
            int m=0;
            for(int j=0;j<T.length();j++){
                if(T.substring(j,j+1).equals(J.substring(j,j+1))){m++;}
            }
            if (m>M){M=m;}
        }
        System.out.println(T.length()-M);
    }}