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
import java.util.*;
public class Main{
 public static void main(String[] args){
   Scanner sc = new Scanner(System.in);
   int N = sc.nextInt();
   int[] Ai = new int[N];
   for(int i = 0;i<N;i++) Ai[i] = sc.nextInt()-(i+1); 
   Arrays.sort(Ai);
   long sum =0;
   int b ;
   long min ;
   if(N%2==1)
   {
     b = Ai[N/2];
     for(int i = 0;i<N;i++)
     {
       sum+=Math.abs(Ai[i]-b);
     }
     min = sum;
   }
   else
   {
     b = Ai[N/2];
     for(int i = 0;i<N;i++)
     {
       sum+=Math.abs(Ai[i]-b);
     }
     min = sum;
     b = Ai[(N/2)-1];
     for(int i = 0;i<N;i++)
     {
       sum+=Math.abs(Ai[i]-b);
     }
     if(min>sum) min = sum;
   }  
   System.out.println(min);
 }
}