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;
long long ans = 0;
long long a[100050];
int n;
inline void get_ready() {
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  sort(a + 1, a + n + 1);
}
inline void solve() {
  for (int i = 1; i <= 32; i++) {
    long long cnt = 1 << i;
    if (cnt > 2 * a[n]) break;
    for (int j = 1; j <= n - 1; j++) {
      int x1 = lower_bound(a + j + 1, a + n + 1, cnt - a[j]) - a;
      int x2 = upper_bound(a + j + 1, a + n + 1, cnt - a[j]) - a;
      if (x1 == n + 1) continue;
      ans += x2 - x1;
    }
  }
  cout << ans << endl;
}
int main() {
  std::ios::sync_with_stdio(0);
  get_ready();
  solve();
  return 0;
}
