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 n=s.length();
  int m=t.length();
  int i,j,c,ans=0;
  for(i=0;i<=n-m;i++)
  {
    c=0;
    for(j=i;j<i+m;j++)
    {
      if(s[j]==t[j-i])
         c++;
    }
    ans=max(ans,c);
  }
  cout<<m-ans;
  return 0;
}
