Kuroni and Antihype
Description
Kuroni isn't good at economics. So he decided to found a new financial pyramid called Antihype. It has the following rules:
- You can join the pyramid for free and get $0$ coins.
- 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.
Input
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
Output exactly one integer — the maximum possible combined gainings of all $n$ people.
Samples
3
1 2 3
2
Note
Only the first and second persons are friends. The second can join Antihype and invite the first one, getting $2$ for it.