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)

def getMedian(data):
    N = len(data)
    data.sort()
    if N % 2 == 0:
        median1 = N / 2
        median2 = N / 2 + 1
        median1 = int(median1) - 1
        median2 = int(median2) - 1
        return int((data[median1] + data[median2]) / 2)
    else:
        median = (N + 1) / 2
        median = int(median) - 1
        return int(data[median])


int(input())
A = list(map(int, input().split()))
B = []
for i in range(len(A)):
    B.append(A[i] - i - 1)

median = getMedian(B)

ans = 0

for b in B:
    ans += abs(b - median)

print(ans)