P6102 [EER2] E-Operation

On a certain “e-e” day, CYJian encountered an “e-operation” problem. CYJian found that he could not solve it, so he decided to start from scratch and study the puzzling “e-operation”.

First, CYJian wrote a sequence $a$ of length $n$. Then he had a sudden idea and wrote down the following puzzling expression: $$\sum_{i=1}^{n}\sum_{j=1}^{n}\sum_{k=1}^{n}\sum_{l=1}^{n} (a_i\ {\rm or}\ a_j)\ {\rm xor}\ (a_k\ {\rm and}\ a_l)$$ CYJian thought this was a simple expression of “e-operation”, and it took him $114514{\rm s}$ with a calculator to compute the answer. To prove that you can outperform $114514$ CYJian, please compute the value of this expression within $1{\rm s}$. You only need to output the value modulo $2^{32}$.

The first line contains a positive integer $n$, denoting the length of the sequence. The second line contains $n$ non-negative integers; the $i$-th number is $a_i$.

Output one non-negative integer, representing the value of the expression given in the description.

Explanation for Sample 1: $(1\ {\rm or}\ 1)\ {\rm xor}\ (1\ {\rm and}\ 1) = 0$. $(1\ {\rm or}\ 1)\ {\rm xor}\ (1\ {\rm and}\ 2) = 1$. $(1\ {\rm or}\ 1)\ {\rm xor}\ (2\ {\rm and}\ 1) = 1$. $(1\ {\rm or}\ 1)\ {\rm xor}\ (2\ {\rm and}\ 2) = 3$. $(1\ {\rm or}\ 2)\ {\rm xor}\ (1\ {\rm and}\ 1) = 2$. $(1\ {\rm or}\ 2)\ {\rm xor}\ (1\ {\rm and}\ 2) = 3$. $(1\ {\rm or}\ 2)\ {\rm xor}\ (2\ {\rm and}\ 1) = 3$. $(1\ {\rm or}\ 2)\ {\rm xor}\ (2\ {\rm and}\ 2) = 1$. $(2\ {\rm or}\ 1)\ {\rm xor}\ (1\ {\rm and}\ 1) = 2$. $(2\ {\rm or}\ 1)\ {\rm xor}\ (1\ {\rm and}\ 2) = 3$. $(2\ {\rm or}\ 1)\ {\rm xor}\ (2\ {\rm and}\ 1) = 3$. $(2\ {\rm or}\ 1)\ {\rm xor}\ (2\ {\rm and}\ 2) = 1$. $(2\ {\rm or}\ 2)\ {\rm xor}\ (1\ {\rm and}\ 1) = 3$. $(2\ {\rm or}\ 2)\ {\rm xor}\ (1\ {\rm and}\ 2) = 2$. $(2\ {\rm or}\ 2)\ {\rm xor}\ (2\ {\rm and}\ 1) = 2$. $(2\ {\rm or}\ 2)\ {\rm xor}\ (2\ {\rm and}\ 2) = 0$. Summing all results, we get the answer $30$. --- **This problem uses bundled testdata.** Constraints: for $100\%$ of the test points, $1 \leq n \leq 5 \times 10^5$, $0 \leq a_i \leq 2^{32}-1$. There are $6$ subtasks in total. The score and settings for each subtask are as follows: Subtask $1$ ($1$ point): Sample 1. Subtask $2$ ($14$ points): $1 \leq n \leq 80$. Subtask $3$ ($25$ points): $0 \leq a_i \leq 80$. Subtask $4$ ($30$ points): $0 \leq a_i \leq 5000$. Subtask $5$ ($25$ points): $1 \leq n \leq 1000$. Subtask $6$ ($5$ points): no special constraints. --- #### Friendly Reminder Please pay attention to the constraints. **If you do not know what the “e-operation” above is, please refer to [here](https://www.luogu.com.cn/paste/oe4a9czd)**. Translated by ChatGPT 5