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

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