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 a, b, c, n, ans;
map<long long, long long> m;
long long d[30];
long long ar[100001];
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> ar[i];
    m[ar[i]]++;
  }
  d[0] = 2;
  for (int i = 1; i < 30; i++) {
    d[i] = d[i - 1] * 2;
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 30; j++) {
      if (d[j] - ar[i] == ar[i]) {
        ans = ans + m[d[j] - ar[i]] - 1;
      } else {
        ans = ans + m[d[j] - ar[i]];
      }
    }
  }
  cout << ans / 2 + ans % 2;
}
