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>

int cmpnum(const void * n1, const void * n2) {
	if (*(long *)n1 > *(long *)n2)
	{
		return 1;
	}
	else if (*(long *)n1 < *(long *)n2)
	{
		return -1;
	}
	else
	{
		return 0;
	}
}

int main(void) {

  long n;
  scanf("%ld", &n);
  long a[n];
  for (long i = 0; i < n; i++) {
    scanf("%ld", &a[i]);
    a[i] -= i+1;
  }
  qsort(a, n, sizeof(long), cmpnum);
  long all = 0;
  for (long i = 1; i < n; i++) {
    all += a[i]-a[0];
  }
  long sadness = all;
  long min = all;
  long level = a[0];
  long width,height;
  for (long i = 0; i < n; i++) {
    if (a[i+1] == level) {
      continue;
    }
    width = i+1;
    if (n-width*2 <= 0) {
      break;
    }
    height = a[i+1]-a[i];
    if (height*(n-width*2) <= sadness) {
      level = a[i+1];
      sadness -= height*(n-width*2);
      min = sadness;
    } else {
      height = sadness/(n-width*2);
      level += height;
      sadness -= height*(n-width*2);
      if (sadness <= min) {
        min = sadness;
      }
      sadness = -(sadness-(n-width*2));
      if (sadness <= min) {
        min = sadness;
      }
      break;
    }
  }
  printf("%ld\n", min);

  return 0;
}