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: Wrong Answer)

#include <math.h>
#include <stdio.h>

int main() {
  int N, sum = 0, temp, A[200000], kouho, sa[3] = {0, 0, 0}, ans;
  scanf("%d", &N);
  for (int i = 0; i < N; i++) {
    scanf("%d", &temp);
    temp -= i;
    A[i] = temp;
    sum += temp;
  }
  kouho = sum / N;
  for (int i = 0; i < N; i++) {
    sa[0] += abs(A[i] - kouho - 1);
  }
  for (int i = 0; i < N; i++) {
    sa[1] += abs(A[i] - kouho);
  }
  for (int i = 0; i < N; i++) {
    sa[2] += abs(A[i] - kouho + 1);
  }
  ans = (sa[0] < sa[1]) ? sa[0] : sa[1];
  ans = (ans < sa[2]) ? ans : sa[2];
  printf("%d", ans);

  return 0;
}

int abs(int N) {
  if (N < 0) N *= -1;
  return N;
}