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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cstdio>
#include <vector>
#include <algorithm>

#define all(v) (v).begin(), (v).end()
using namespace std;

int main()
{
    int no_of_elements;
    scanf("%d", &no_of_elements);

    vector <int> A(no_of_elements);
    vector <int> sorted_A(no_of_elements);
    for(int i = 0; i < no_of_elements; i++)
    {
        scanf("%d", &A[i]);
        A[i] -= (i + 1);

        sorted_A[i] = A[i];
    }

    sort(all(sorted_A));

    int median_index = no_of_elements/2 + no_of_elements%2 - 1;
    int median = sorted_A[median_index];

    long long answer = 0;
    for(int i = 0; i < no_of_elements; i++)
        answer += abs(A[i] - median);

    printf("%lld\n", answer);

    return 0;
}