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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
int main() {
    int n,b,sum = 0,sumr = 0,sumrr = 0;
    double bb;
    scanf("%d",&n);
    int a[n];
    for(int i = 0;i < n;i++) scanf("%d",&a[i]);
    for(int i = 0;i < n;i++) a[i] -= i + 1;
    for(int i = 0;i < n;i++) sum += a[i];
    b = sum / n;
    bb = sum / n;
//     if(bb - b >= 0.5) b += 1;
//     printf("%d",b);
    for(int i = 0;i < n;i++) sumr += abs(a[i] - b);
    for(int i = 0;i < n;i++) sumrr += abs(a[i] - b - 1);
    if(sumr < sumrr) printf("%d",sumr);
    else printf("%d",sumrr);
    return 0;
}