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 < n; ++i)
using namespace std;

int main(){
  string s, t; cin >> s >> t;
  int n = s.size(), m = t.size(), a = 1e9;
  rep(i, n-m+1){
    int u = 0;
    rep(j, m) if(s[i+j] != t[j]) ++u;
    a = min(a, u);
  }
  cout << a << "\n";
  return 0;
}