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.