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 ans = 1e9;
  for(size_t i = 0; i+t.length() <= s.length(); ++i){
    int d = 0;
    for(size_t j = 0; j < t.length(); ++j){
      d += s[i+j] != t[j];
    }
    ans = min(ans,d);
  }
  cout << ans << endl;
}
