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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from collections import Counter


def solve(string):
    n, *a = map(int, string.split())
    a = [_a - i - 1 for i, _a in enumerate(a)]
    counts = Counter(a)
    max_count = max(counts.values())
    search = [k for k, v in counts.items() if v == max_count]
    ans = 2 * n * 10**9
    for s in search:
        ans = min(ans, sum([abs(_a - s) for _a in a]))
    mean = sum(a) // n
    for i in range(2):
        ans = min(ans, sum([abs(_a - mean - i) for _a in a]))
    return str(ans)


if __name__ == '__main__':
    print(solve("\n".join([input(), input()])))