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 <stdio.h>
#include <stdlib.h>
int comp(const void *a, const void *b) {
    return *(int*)a - *(int*)b;
}
int main() {
  int n,a[200000],i,b,ans[3]={0},max=1,c=1,p;
  double sum=0;
  scanf("%d",&n);
  for (i=0; i<n; i++) {
    scanf("%d",&a[i]);
    a[i]-=i+1;
  }
  p=n/2;
  qsort(a, n, sizeof(int), comp);
  for (i=0; i<n-1; i++) {
    if (a[i]==a[i+1]) {
      c++;
    } else {
      if (max<c) {
        max=c;
        p=i;
      }
      c=1;
    }
  }
  b=a[p];
  for (i=0; i<n; i++) {
    ans[0]+=abs(a[i]-b);
    ans[1]+=abs(a[i]-b-1);
    ans[2]+=abs(a[i]-b+1);
  }
  qsort(ans, 3, sizeof(int), comp);
  printf("%d\n",ans[0]);
  return 0;
}