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>

int abs(a)
{
    return (a > 0) ? a : -a;
}

int main()
{
    int n;  scanf("%d", &n);
    int a[n];


    int i;
    int suma = 0;
    for(i = 0; i < n; i++){
        scanf("%d", &a[i]);
        a[i] -= i + 1;
        suma += a[i];
    }

    int b1, b2;
    if(suma / n > 0){
        b1 = suma / n + 1;
        b2 = suma / n;
    }
    else{
        b1 = suma / n - 1;
        b2 = suma / n;
    }

    int sum1 = 0, sum2 = 0;
    for(i = 0; i < n; i++){
        sum1 += abs(a[i] - b1);
        sum2 += abs(a[i] - b2);
    }

    printf("%d\n", (sum1 < sum2) ? sum1 : sum2);

    return 0;
}