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;
  int arr[n];
  map<int, long long> m;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    m[arr[i]]++;
  }
  long long ans = 0;
  for (int i = 1; i < 32; i++) {
    long long a = pow(2, i);
    for (int j = 0; j < n; j++) {
      if (arr[j] < a) {
        if (m[a - arr[j]] != 0) {
          if ((a / 2) != arr[j]) {
            ans = ans + m[a - arr[j]];
          } else {
            ans = ans + ((m[arr[j]] - 1));
          }
        }
      }
    }
  }
  ans /= 2;
  cout << ans << endl;
}
