G. Kuroni and Antihype
time limit per test
3 seconds
memory limit per test
256 megabytes
standard input
standard output

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?


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.


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

1 2 3

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