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.Scanner;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			char[] s = scanner.next().toCharArray(), t = scanner.next().toCharArray();
			System.out.println(t.length
					- IntStream.rangeClosed(0, s.length - t.length).map(i -> calcResult(i, s, t)).max().getAsInt());
		}
	}

	private static int calcResult(int from, char[] s, char[] t) {
		int result = 0;
		for (int i = 0; i < t.length; i++) {
			result += (s[from + i] == t[i]) ? 1 : 0;
		}
		return result;
	}
}
