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;
struct union_find {
  vector<int> data;
  int components = 0;
  union_find(int n = -1) {
    if (n >= 0) init(n);
  }
  void init(int n) {
    data.assign(n + 1, -1);
    components = n;
  }
  int find(int x) { return data[x] < 0 ? x : data[x] = find(data[x]); }
  int get_size(int x) { return -data[find(x)]; }
  bool unite(int x, int y) {
    x = find(x);
    y = find(y);
    if (x == y) return false;
    if (-data[x] < -data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    components--;
    return true;
  }
};
const int BITS = 18;
int freq[1 << BITS];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  freq[0] = 1;
  int N;
  cin >> N;
  long long answer = 0;
  for (int i = 0; i < N; i++) {
    int a;
    cin >> a;
    freq[a]++;
    answer -= a;
  }
  union_find UF(1 << BITS);
  auto &&contribution = [&](int a, int b) {
    if (freq[a] == 0 || freq[b] == 0 || !UF.unite(a, b)) return 0;
    int edges = freq[a] + freq[b] - 1;
    freq[a] = freq[b] = 1;
    return edges;
  };
  for (int sum = (1 << BITS) - 1; sum >= 0; sum--)
    for (int mask = sum; mask > (sum ^ mask); mask = (mask - 1) & sum) {
      int other = sum ^ mask;
      int edges = contribution(mask, other);
      answer += (long long)edges * sum;
    }
  cout << answer << '\n';
}