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 ascSort(const void* v1, const void* v2);

int main (void)
{
   int n,i,b;
   long int min_sadness=0;
   int *p,*q;

   scanf("%d",&n);

   p=(int*)malloc(sizeof(int)*n);
   q=(int*)malloc(sizeof(int)*n);

   for(i=0;i<n;i++)
   scanf("%d",p+i);

   for(i=0;i<n;i++)
   *(q+i)=*(p+i)-(i+1);

   qsort(q, n, sizeof(q[0]), ascSort);

   b=*(q+(n+1)/2);
   for(i=0;i<n;i++)
   min_sadness+=abs(*(q+i)-b);

   printf("%d\n",min_sadness);
   free(p);

   return 0;
}
int ascSort(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;
    }
}