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 s = S.size(), t = T.size(), ans{1000};
  for (int i = 0; i <= s - t; ++i) {
    int c{t};
    for (int j = 0; j != t; ++j) {
      if (S[i+j] == T[j]) --c;
    }
    ans = min(ans, c);
  }
  cout << ans << endl;
}
