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 Python (3.4.3) (judge verdict: Wrong Answer)

import numpy as np
n = int(input())
inputs = [int(i) for i in input().split()]
a = np.array(inputs)

min_num = 100000000000
z = a - np.array(range(1, n + 1))
nums = list(set(inputs))
#allnum = nums + list(np.array(nums) * (-1)) + [0]
allnum = []
allnum.append(min(abs(z)))
allnum.append(-min(abs(z)))
allnum.append(max(abs(z)))
allnum.append(-max(abs(z)))


for x in allnum:
  min_sum = sum(abs(z - np.ones(len(a)) * x))
  if min_sum < min_num:
    min_num = min_sum

print(int(min_num))