Problem Statement

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.

Sample Input 1

cabacc
abc

Sample Output 1

1

For example, changing the fourth character a in $S$ to c will match the second through fourth characters in $S$ to $T$.

Since $S$ itself does not have $T$ as its substring, this number of changes - one - is the minimum needed.

Sample Input 2

codeforces
atcoder

Sample Output 2

6