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(void){
  string s,t;cin>>s>>t;
  int cnt,min=1000;
  int size1=s.size(),size2=t.size();
  for(int i=0; i<(size1-size2+1); ++i){
    cnt=size2;
    for(int j=0; j<size2; ++j) if(s[i+j]==t[j]) --cnt;
    if(min>cnt) min=cnt;
  }
  cout<<min<<endl;
  return 0;
}
