Y is alone too and has a permutation \(p_1, p_2, ..., p_n\) of numbers from \(1\) to \(n\).

Y thinks that a permutation \(p_1, p_2, ..., p_n\)  beautifulness is defined as value of \(\sum |p_i - i|, 1 \leq i \leq n\).

Y can swap two elements of the permutation at most once, what is the maximum beautifulness that Y can get?

Input

First line contains only \(n\).

Second line contains the permutation \(p_1, p_2, ..., p_n\) separated by space.

\(1 \leq n \leq 10^5\)

\(1 \leq p_i \leq n\), all \(p_i\) are distinct.

Output

The only line of output contains an integer, maximum beautifulness that Y can get.