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)

#include <stdio.h>
#include <stdlib.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,n,i,j,b;
  int ans;
  int A[150], num[150],tmp[150];
  scanf("%d", &N);
  for(i = 0;i < N;i++){
      scanf("%d", &A[i]);
  }
  for(n = 0;n < N;n++){
    num[n] = A[n]-(n+1);
  }

  qsort(num, N, sizeof(int), cmp_int);

  if(N % 2 == 1){
    b = num[N / 2];
  } else {
    b = (num[N / 2] + num[1 + (N / 2)]) / 2;
  }
  for(n = 0;n < N; n++){
    tmp[n] = A[n] - (b + n+1);
    tmp[n] = abs(tmp[n]);
    ans += tmp[n];
  }
  printf("%d", ans);

  return 0;
}