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>
#define rep(i,n) for (int i=0;i<(int)(n);i++)
using namespace std;

int main()
{
  string S,T;
  cin>>S>>T;
  int a=1e9;
  rep(si,S.size()-T.size()+1){
    int cnt=0;
    rep(ti,T.size()){
      if(S[si+ti]!=T[ti]) cnt++;
    }
    a = min(a,cnt);
  }
  cout<<a<<endl;
  return 0;
}