CF1305G.Kuroni and Antihype

Kuroni isn't good at economics. So he decided to found a new financial pyramid called Antihype. It has the following rules:

1. You can join the pyramid for free and get $0$ coins.
2. If you are already a member of Antihype, you can invite your friend who is currently not a member of Antihype, and get a number of coins equal to your age (for each friend you invite).

$n$ people have heard about Antihype recently, the $i$-th person's age is $a_i$. Some of them are friends, but friendship is a weird thing now: the $i$-th person is a friend of the $j$-th person if and only if $a_i \text{ AND } a_j = 0$, where $\text{AND}$ denotes the bitwise AND operation.

Nobody among the $n$ people is a member of Antihype at the moment. They want to cooperate to join and invite each other to Antihype in a way that maximizes their combined gainings. Could you help them?

库洛尼不擅长经济学，因此他决定创立一种名为“反热潮”（Antihype）的新型金融传销模式。其规则如下：

1. 你可以免费加入该传销模式，并获得 $0$ 枚金币；
2. 若你已是“反热潮”的成员，则可邀请一位当前尚未加入“反热潮”的朋友，并获得等于你年龄数量的金币（每成功邀请一位朋友，即获得相应金币）。

最近有 $n$ 个人听说了“反热潮”，其中第 $i$ 个人的年龄为 $a_i$。他们中部分人互为朋友，但如今友谊关系十分特殊：当且仅当 $a_i \text{ AND } a_j = 0$ 时，第 $i$ 个人才是第 $j$ 个人的朋友（其中 $\text{AND}$ 表示按位与运算）。

目前，这 $n$ 个人中尚无一人是“反热潮”的成员。他们希望通力合作，以某种顺序加入并相互邀请，使得所有人获得的金币总数最大化。你能帮帮他们吗？

The first line contains a single integer $n$ ($1\le n \le 2\cdot 10^5$) — the number of people.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0\le a_i \le 2\cdot 10^5$) — the ages of the people.

第一行包含一个整数 $n$（$1\le n \le 2\cdot 10^5$）—— 表示人数。

第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$0\le a_i \le 2\cdot 10^5$）—— 表示每个人的年龄。

Output exactly one integer — the maximum possible combined gainings of all $n$ people.

输出一个整数——即所有 $n$ 个人可能获得的最大总收益。

Only the first and second persons are friends. The second can join Antihype and invite the first one, getting $2$ for it.

只有第一人和第二人是朋友。第二人可以加入 Antihype 并邀请第一人，从而获得 $2$ 分。