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: Runtime Error)

N = int(input())
A = list(map(int, input().split()))
b = 0
ans = 10**10

def calabs(n, b, a):
    return abs(a[n] - (b + (n + 1)))

diff1 = [calabs(i, -1, A) for i in range(N)]
diff2 = [calabs(i, 0, A) for i in range(N)]
diff3 = [calabs(i, 1, A) for i in range(N)]

# print(sum(diff1), sum(diff2), sum(diff3))

if sum(diff1) <= sum(diff2) <= sum(diff3):
    tmp = -1
elif sum(diff1) >= sum(diff2) >= sum(diff3):
    tmp = 1

while True:
    diff = [calabs(i, b, A) for i in range(N)]
    
    if ans >= sum(diff):
        ans = sum(diff)
        # print(ans)
        b += tmp
    else:
        print(ans)
        break