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;
  int res=1000, sum=0;
  cin>>a>>b;
  for(int i=0;i<=a.size()-b.size();i++){
    sum=0;
    for(int j=0;j<b.size();j++){
      if(a[i+j] != b[j]) sum++;
    }
    res=min(res,sum);
  }
  cout<<res<<endl;
}