A13493 | AND, OR and square sum

Gottfried learned about binary number representation. He then came up with this task and presented it to you.

You are given a collection of $n$ non-negative integers $a_1, \ldots, a_n$ . You are allowed to perform the following operation: choose two distinct indices $1 \leq i, j \leq n$ . If before the operation $a_i = x$ , $a_j = y$ , then after the operation $a_i = x~\mathsf{AND}~y$ , $a_j = x~\mathsf{OR}~y$ , where $\mathsf{AND}$ and $\mathsf{OR}$ are bitwise AND and OR respectively (refer to the Notes section for formal description). The operation may be performed any number of times (possibly zero).

After all operations are done, compute $\sum_{i=1}^n a_i^2$ — the sum of squares of all $a_i$ . What is the largest sum of squares you can achieve?

The first line contains a single integer $n$ ( $1 \leq n \leq 2 \cdot 10^5$ ).

The second line contains $n$ integers $a_1, \ldots, a_n$ ( $0 \leq a_i < 2^{20}$ ).

Print a single integer — the largest possible sum of squares that can be achieved after several (possibly zero) operations.