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;
#define REP(i, n) for(int i=0; i<(int)(n); i++)
int main(){
string S, T; cin >> S >> T; int c=0, ans=T.size();
REP(i, S.size()-T.size()+1){ 
  c=0;
  REP(j, T.size()){ if(S[i+j]!=T[j]){ c++; } }
  ans=min(c, ans);
}
cout << ans << "\n";
}