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;
class map<int, int> sum;
int main() {
  int n, a[100005], i, j, pow[34], b;
  long long cou;
  pow[1] = 1;
  for (i = 2; i <= 32; i++) pow[i] = pow[i - 1] * 2;
  scanf("%d", &n);
  cou = 0;
  for (i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    sum[a[i]]++;
  }
  for (i = 1; i <= n; i++) {
    for (j = 2; j <= 32; j++) {
      if (pow[j] > a[i]) {
        b = pow[j] - a[i];
        if (sum[b] > 0) {
          if (b == a[i])
            cou = cou + sum[b] - 1;
          else
            cou = cou + sum[b];
        }
      }
    }
  }
  cout << cou / 2 << '\n';
  return 0;
}
