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;
int main() {
  long long int two[31];
  for (int i = 0; i < 31; i++) two[i] = 1 << i;
  int n;
  cin >> n;
  int ara[n], a;
  map<int, int> m;
  for (int i = 0; i < n; i++) {
    cin >> ara[i];
    m[ara[i]]++;
  }
  long long ans = 0, need;
  for (int i = 0; i < n; i++) {
    a = ara[i];
    for (int i = 0; i < 31; i++) {
      need = two[i] - a;
      map<int, int>::iterator it = m.find(need);
      if (it != m.end()) {
        ans += (it->second);
        if (a == need) ans--;
      }
    }
    m[a]--;
  }
  cout << ans << endl;
  return 0;
}
