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 (3.8.2) (judge verdict: Accepted)

n = int(input())
a_list = list(map(int,input().split()))
ans_list = []
for i in range(len(a_list)):
    ans_list.append(a_list[i] - i - 1)
import numpy as np
if len(ans_list)% 2 == 0:
    ans_list1 = sorted(ans_list)
    number1 = ans_list1[n//2]
    number2 = ans_list1[n//2 + 1]
    
    ans1 = 0
    ans2 = 0
    for i in ans_list:
        ans1 += abs(i - number1)
        ans2 += abs(i - number2)
    print(min(ans1 , ans2))
else:
    cary = ans_list
    number = int(np.median(cary))
    ans = 0
    for i in ans_list:
        ans += abs(i - number)
    print(ans)