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 PyPy3 (2.4.0) (judge verdict: Accepted)

n = input()
n = int(n)
a = input().split()
a = [int(aa) for aa in a]

ans = 10000000000000000

l = -100000000000
r =  100000000000

for count in range(100):
    mid = (l + r) // 2
    temp = 0
    for i in range(n):
        temp1= abs(a[i] - (mid + i + 1))
        temp2= abs(a[i] - ((mid - 1) + i + 1))
        temp += temp1 - temp2
    if temp > 0:
        r = mid
    else:
        l = mid
for b in range(l, r + 1):
    temp = 0
    for i in range(n):
        temp += abs(a[i] - (b + i + 1))
    ans = min(ans, temp)
print(ans)