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: Runtime Error)

/*
https://beta.atcoder.jp/contests/abc102/tasks/arc100_a
*/

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

#define MAX 20000000

int main() {
  long n;
  long a[MAX] = {};
  long flag[MAX] = {};
  long i;
  long b = 0;

  scanf("%ld", &n);

  for(i = 1; i <= n; i++){
    scanf("%ld", &a[i]);
  }

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

  int count = 0;
  for(i = 0; i <= n; i++){
    if(count < flag[i]){
      count = flag[i];
      b = -1*i;
      // printf("%d", b);
    }
  }

  long ans = 0;

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

  printf("%ld", ans);

  return 0;
}