Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

5
2 2 3 5 5

Sample Output 1

2

If we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.
Any choice of b does not make the sadness of Snuke less than 2, so the answer is 2.

Sample Input 2

9
1 2 3 4 5 6 7 8 9

Sample Output 2

0

Sample Input 3

6
6 5 4 3 2 1

Sample Output 3

18

Sample Input 4

7
1 1 1 1 2 3 4

Sample Output 4

6

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
 
int cmp_int(const void* v1, const void* v2)
{
  const int _v1 = *((const int*)v1);
  const int _v2 = *((const int*)v2);

  if ( _v1 > _v2 ) {
    return 1;
  } else if ( _v1 < _v2 ) {
    return -1;
  } else {
    return 0;
  }
}
 
int main(void){
    int n;
    scanf("%d",&n);
    int a[n],b[n];
    for (int i=0; i<n; i++){
        scanf("%d",&a[i]);
        b[i]=a[i]-(i+1);
    }
    qsort (b,n,sizeof(int),cmp_int);
    long long int ans1=0,ans2=0;
    if (n%2==0){
        for (int i=0; i<n; i++){
            ans1+=abs(b[i]-b[n/2-1]);
            ans2+=abs(b[i]-b[n/2]);
        }
        if (ans1<ans2){
            printf ("%lld\n",ans1);
        } else {
            printf ("%lld\n",ans2);
        }
    } else {
        for (int i=0; i<n; i++){
            ans1+=abs(b[i]-b[(n+1)/2-1]) ;
        }
        printf ("%lld\n",ans1) ;
    }
	return 0 ;
}