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(){
    string s,t;
    cin>>s>>t;
    int ans=1000;
    for(int i=0;i<=s.size()-t.size();i++){
        int x=0;
        for(int j=0;j<t.size();j++)if(s[i+j]!=t[j])x++;
        ans=min(ans,x);
    }
    cout<<ans<<endl;
    return 0;
}