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 <bits/stdc++.h>
using namespace std;

int main() {
  string S, T;
  cin >> S >> T;
  int C=0, m=1000000;
  for (int i=0; i<=S.size()-T.size(); i++) {
    C=0;
    for (int j=0; j<T.size(); j++) {
      if (S[i+j]!=T[j]) {
        C++;
      }
    }
    m=min(m, C);
  }
  cout << m << endl;
}