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-----
5
2 2 3 5 5

-----Sample Output-----
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.

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