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 N = 2e5 + 2;
int t, n, a[32], x[N];
long long ans;
int main() {
  std::ios::sync_with_stdio(false);
  cin.tie();
  cout.tie();
  for (int i = 0; i < 31; i++) {
    a[i] = 1 << i;
  }
  cin >> n;
  for (int i = 0; i < n; i++) cin >> x[i];
  sort(x, x + n);
  int idx;
  for (int i = 0; i < 31; i++) {
    for (int j = 0; j < n && x[j] <= a[i]; j++) {
      idx = lower_bound(x, x + n, a[i] - x[j]) - x;
      if (idx != j && x[idx] == a[i] - x[j])
        ans += upper_bound(x, x + n, a[i] - x[j]) - x - idx;
    }
  }
  ans >>= 1;
  cout << ans;
  return 0;
}
