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>

int main(){
  std::string S,T;
  std::cin>>S>>T;
  int max = 0;
  for (int i = 0; i < S.size()-T.size()+1; i++){
    int counter = 0;
    for (int j = 0; j < T.size(); j++)
      if (S[i+j]==T[j]) counter++;
    if (max<counter) max = counter;
  }
  std::cout<<T.size()-max<<std::endl;
}