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: Wrong Answer)

let () =
  let rec charlist_of_string str n i =
    if i = n then [] else str.[i] :: charlist_of_string str n (i+1) in
  Scanf.scanf "%s\n%s\n" @@ fun s t ->
  let slst = charlist_of_string s (String.length s) 0 in
  let tlst = charlist_of_string t (String.length t) 0 in
  let ans = ref max_int in
  let rec check lst1 lst2 ans = match lst1, lst2 with
    | [], [] -> ans
    | _,  [] -> raise Not_found
    | [], _  -> raise Not_found
    | h1 :: t1, h2 :: t2 -> if h1 = h2 then check t1 t2 ans else check t1 t2 (ans + 1) in
  for start = 0 to (String.length s) - (String.length t) - 1 do
    let buf = check (Array.to_list (Array.sub (Array.of_list slst) start (String.length t))) tlst 0 in
    if buf < !ans then ans := buf
  done;
  Printf.printf "%d\n" !ans