Snuke has an integer sequence A of length N.

He will freely choose an integer b. Here, he will get sad if A_i and b+i are far from each other. More specifically, the sadness of Snuke is calculated as follows:

* abs(A_1 - (b+1)) + abs(A_2 - (b+2)) + ... + abs(A_N - (b+N))



Here, abs(x) is a function that returns the absolute value of x.

Find the minimum possible sadness of Snuke.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the minimum possible sadness of Snuke.

Examples

Input

5
2 2 3 5 5


Output

2


Input

9
1 2 3 4 5 6 7 8 9


Output

0


Input

6
6 5 4 3 2 1


Output

18


Input

7
1 1 1 1 2 3 4


Output

6
#include <bits/stdc++.h>
using namespace std;
 
int main() {
  int N;
  cin >> N;
  vector<int> A(N);
  for (int i=0;i<N;i++){
    int x;
    cin >> x;
    A[i]=x-(i+1);
  }
  sort(A.begin(),A.end());
  int x=A[(N+1)/2-1];
  long long ans=0;
  for (int i=0;i<N;i++){
    ans+=(long long)abs(A[i]-x);
  }
  cout << ans << endl;
}