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>
#include <string.h>
#include <math.h>

int sort(const void *a, const void *b){
    return *(int*)a-*(int*)b ;
}

int main(void){
    int n;
    scanf("%d",&n);
    int a1[n],a[n],tmp[n];
    for (int i=0; i<n; i++){
        scanf("%d",&a1[i]);
        a[i]=a1[i]-(i+1);
    }
    qsort (a,n,sizeof(int),sort);

    for (int i=0; i<n; i++){
        tmp[i]=0;
        if (a[i]!=a[i-1] || i==0){
            for (int j=0; j<n; j++){
                tmp[i]+=abs(a[j]-a[i]);
            }
        } else {
            tmp[i]=tmp[i-1];
        }
    }
    qsort (tmp,n,sizeof(int),sort);
    printf ("%d\n",tmp[0]);
    
    return 0 ;
}