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 = 1e5 + 5;
map<long long, int> mp;
long long f[34];
int a[N];
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i <= 30; i++) f[i] = 1 << i;
  sort(a, a + n);
  long long ans = 0;
  for (int i = 0; i < n - 1; i++) {
    for (int j = 0; j <= 30; j++) {
      int t = f[j] - a[i];
      int l = lower_bound(a + 1 + i, a + n, t) - a;
      if (a[l] == t) {
        int r = upper_bound(a + i + 1, a + n, t) - a;
        ans += r - l;
      }
    }
  }
  cout << ans << endl;
  return 0;
}
