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: Time Limit Exceeded)

memo={}
def calc(A, b):
    score = memo.get(b, None)
    if not score is None:
        return score
    score = sum(abs(a-b) for a in A)
    memo[b] = score
    return score

def findmin(A, l, u):
    if l + 1 == u:
        return min(calc(A, l), calc(A, u))
    if l == u:
        return calc(A, l)
    d = (u-l)//3
    if d == 0:
        return min(calc(A, i) for i in range(l, u+1))
    left, right = l + d, u - d
    sl = calc(A, left) 
    sr = calc(A, right) 
    if sl > sr:
        return findmin(A, left, u)
    else:
        return findmin(A, l, right)

def solve(A):
    A = sorted(a-(i+1) for i, a in enumerate(A))
    return findmin(A, A[0], A[-1])

#solve(list(range(1000, 2*10**5)))
N = int(input())
A = [int(x) for x in input().split()]

#abs(A1-(b+1)) + abs(Ai-(b-i)) + abs(AN-(b-N))


# b1 = A[0]    ならば (A[i]-b1) >= 0
# b2 = A[0] -1 ならば (A[i]-b2) > (A[i]-b1) >= 0 なので、スコアは大きくなる

# b = A[-1] ならば (A[i]-b) <= 0

print(solve(A))