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 A,B;
  cin>>A>>B;
  int a,b;
  int ans=1000;
  a=A.size();
  b=B.size();
  for(int i=0; i<a-b+1; i++){
    int d=0;
    for(int j=0; j<b;j++){
      if(A.at(j+i)!=B.at(j))
        d++; 
    }
    if(d<=ans)
      ans=d;
  }
  cout<<ans<<endl;
}

