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 dx[8] = {-1, 1, 0, 0, 1, 1, -1, -1}, dy[8] = {0, 0, -1, 1, 1, -1, 1, -1};
char dc[4] = {'N', 'S', 'W', 'E'};
long long int a[300005];
map<long long int, long long int> m;
int main() {
  long long int n, p, q, ans = 0;
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) {
    p = log2(a[i]);
    for (long long int j = p + 1; j <= 31; j++) {
      q = (1LL << j);
      ans += m[q - a[i]];
    }
    m[a[i]]++;
  }
  cout << ans << endl;
}
