Problem: 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  AND  a_j = 0, where AND denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).

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? 

Input

The first line contains a single integer n (1≤ n ≤ 2⋅ 10^5) — the number of people.

The second line contains n integers a_1, a_2, ..., a_n (0≤ a_i ≤ 2⋅ 10^5) — the ages of the people.

Output

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

Example

Input


3
1 2 3


Output


2

Note

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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n;
int pl = (1 << 18);
int a[300005], f[300005];
long long ans = 0;
int find(int k) { return (f[k] == k) ? k : f[k] = find(f[k]); }
void link(int u, int v, int w) {
  if (!(a[u] && a[v])) return;
  u = find(u);
  v = find(v);
  if (u == v) return;
  ans = (ans + 1ll * w * (a[u] + a[v] - 1));
  a[v] = 1;
  f[u] = v;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    int x;
    scanf("%d", &x);
    a[x]++;
    ans = ans - x;
  }
  a[pl] = 1;
  f[pl] = pl;
  for (int i = 0; i < pl; i++) f[i] = i;
  for (int i = pl - 1; i; i--) {
    for (int r = i; r; r = (r - 1) & i) {
      link(r, i ^ r, i);
    }
    link(i, pl, i);
  }
  printf("%lld\n", ans);
}