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>

long abso(long);
int int_sort(const void *, const void *);

int main()
{
  long n, a[200000], i, b, ans;

  scanf("%ld", &n);

  for (i = 0; i < n; ++i)
  {
    scanf("%ld", &(a[i]));
  }

  for(i = 0; i < n; ++i)
  {
    a[i] -= i + 1;
  }

  qsort((void *)a, n, sizeof(a[0]), int_sort);

  if (n % 2 == 0)
  {
    b = a[n / 2 - 1];
  }
  else
  {
    b = a[(n + 1) / 2 - 1];
  }

  ans = 0;
  for (i = 0; i < n; ++i)
  {
    ans += abs(a[i] - b);
  }

  printf("%ld\n", ans);

  return 0;
}

long abso(long a)
{
  if (a < 0) a = - a;

  return a;
}

int int_sort( const void * a , const void * b )
{
  if (*( long *)a < *(long *)b)
  {
    return -1;
  }
  else if (*( long *)a == *(long *)b)
  {
    return 0;
  }
  return 1;
}