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;
  vector<int>v;
  cin>>s>>t;
  int sl=s.size(),tl=t.size();
  for(int i=0;i<=sl-tl;i++)
  { int cnt=0; 
    for(int j=0;j<tl;j++)
    if(s[i+j]!=t[j]) cnt++;
   
   v.push_back(cnt);
  }
  sort(v.begin(),v.end());
  cout<<v[0];
}