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
#include<iostream>
using namespace std;

int main() {
  string S, T; cin >> S >> T;
  int N = S.size(), M = T.size();
  int min_s = 10000;
  for (int i = 0; i <= N-M; i++) {
    int c = 0;
    for (int j = 0; j < M; j++) c += (S[i+j] != T[j]);
    min_s = min(min_s, c);
  }
  cout << min_s << endl;
}