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())
a = list(map(int,input().split()))
b = []
cnt = 1
for num in a:
    num -= cnt
    b.append(num)
    cnt += 1
test = [int(np.mean(b))-2,int(np.mean(b))-1,int(np.mean(b)),int(np.mean(b))+1,int(np.mean(b))+2]
ans = []
s = 9999999999999
for i in test:
    cnt = 1
    c = []
    for num in a:
        st = 0
        st = abs(num - (i+cnt))
        c.append(st)
        cnt += 1
    ans.append(np.sum(c))
print(np.min(ans))