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 int ABS(int a){
        return (a>0)?a:-a;
    }
    
    public static int shellsort(int[] X,int N){
    int count=0;
    int h;
    for(h=1;h<N/9;h=3*h+1){
      ;
    }
    
    for(;h>0;h/=3){
      for(int i=h;i<N;i++){
        int j;
        int tmp=X[i];
        for(j=i-h;j>=0&&tmp<X[j];j-=h){
          X[j+h]=X[j];
          count++;
        }
        X[j+h]=tmp;
        count++;
      }
    }
    return count;
  }
  
    public static void main(String[] args) throws Exception {
        Scanner sc=new Scanner(System.in);
        int N=sc.nextInt();
        int[] A=new int[N];
        int MINUS;
        
        for(int i=0;i<N;i++){
            A[i]=sc.nextInt()-i-1;
        }
        
        int S=shellsort(A,N);
        
        if(N%2==1){
            int CENTER=(N+1)/2;
            MINUS=A[CENTER-1];
        }else{
            int CENTER=(N+1)/2;
            MINUS=A[CENTER-1];
        }
        
        Long ANS=0L;
        
        for(int i=0;i<N;i++){
            ANS+=ABS(A[i]-MINUS);
        } 
      
        System.out.println(ANS);
    }
}
