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 <iostream>
using namespace std;
int main() {
    string a,b;cin>>a>>b;
    int m=a.length(),n=b.length(),t=m;
    for(int i=0;i+n<=m;i++)
    {
        int c=0;
        for(int j=0;j<n;j++)
        {
            if(a[i+j]!=b[j])
            c++;
        }
        t=min(t,c);
    }
    cout<<t<<endl;
}
