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: Accepted)

import collections
from statistics import median

n = int(input())
array = list(map(int, input().split()))

for i in range(0, n):
    array[i] = array[i] - (i + 1)
c = collections.Counter(array)
elem = int(c.most_common()[0][0])

# print(c.most_common()[0][0])
# print(array)
# print(elem)
# if c.most_common()[0][1] != 1:
#     # print("test")
#     for j in range(0, n):
#         array[j] = abs(array[j] - elem)
# else:
#     for j in range(0, n):
#         array[j] = abs(array[j])
b = int(median(array))
for j in range(0, n):
    array[j] = int(abs(array[j] - b))

print(sum(array))