Eve, Psyche and the Wife of the Blue MEX

$\textrm{mex}(S)$ is the smallest non-negative integer not contained in the set $S$.

Given $N$ non-negative integers $A_1, A_2, \dots, A_N$, write a program that computes the following value.

$\sum_{i=1}^{N-1} \sum_{j=i+1}^{N} \textrm{mex}(\{A_i, A_j\})$

The first line contains an integer $N$. ($2 \le N \le 200\,000$)

The second line contains $N$ integers $A_1, A_2, \dots, A_N$ separated by spaces. ($0 \le A_i \le 100\,000$)

Print the value the problem asks for.