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() {
  int n;
  cin >> n;
  long long a[n];
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  vector<long long> s;
  for (long long k = 1; k <= 1e12; k *= 2) {
    s.push_back(k);
  }
  long long ans = 0;
  map<long long, long long> m;
  for (auto x : s) {
    m.clear();
    for (int i = 0; i < n; i++) {
      ans += m[x - a[i]];
      m[a[i]]++;
    }
  }
  cout << ans << "\n";
}
