Problem:
Score : 200 points

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

Solution in OCaml (4.10.0) (judge verdict: Accepted)

let () = Scanf.scanf " %s %s" @@ fun s t ->
  Printf.printf "%d\n" @@
  Array.fold_left min max_int @@
  Array.init (String.length s - String.length t + 1) @@ fun i ->
    Array.fold_left ( + ) 0 @@
    Array.init (String.length t) @@ fun j -> if s.[i + j] = t.[j] then 0 else 1