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 ll long long
int main(){
  string s,t; cin>>s>>t; int c=0,d=0;
  int l=t.length(),p=s.length();
  for(int i=0;i<=p-l;i++){
    string z=s.substr(i,l); c=0;
    for(int j=0;j<l;j++){
        if(z[j]==t[j])c++;
    }
    d=max(d,c);
  } cout<<l-d;
}
