You are given n integers a1, a2, ..., an. Find the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2 (i. e. some integer x exists so that ai + aj = 2x).

Input

The first line contains the single positive integer n (1 ≤ n ≤ 105) — the number of integers.

The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2.

Examples

Input

4
7 3 2 1


Output

2


Input

3
1 1 1


Output

3

Note

In the first example the following pairs of indexes include in answer: (1, 4) and (2, 4).

In the second example all pairs of indexes (i, j) (where i < j) include in answer.
#include <bits/stdc++.h>
using namespace std;
const int mod = 1000000007;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int t, n, m, k, q, x, a, b, c, d, w;
  cin >> n;
  vector<long long int> v(n);
  map<long long int, int> map;
  for (int i = 0; i < n; i++) {
    cin >> v[i];
    map[v[i]]++;
  }
  vector<long long int> P;
  a = 2;
  while (a < 1e10) {
    P.push_back(a);
    a *= 2;
  }
  m = P.size();
  long long int ans = 0;
  for (int i = 0; i < n; i++) {
    map[v[i]]--;
    for (int j = 0; j < m; j++) {
      ans += map[P[j] - v[i]];
    }
  }
  cout << ans << "\n";
  return 0;
}
