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.