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 Max = 101101;
long long n;
long long a[Max];
long long ans;
map<long long, long long> have;
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  ans = 0;
  have[a[n]] = 1;
  for (int i = n - 1; i >= 1; i--) {
    long long one = 1;
    for (long long st = 0; st < 34; st++) {
      long long need = (one << st);
      need -= a[i];
      if (have.find(need) != have.end()) ans += have[need];
    }
    if (have.find(a[i]) != have.end())
      have[a[i]]++;
    else
      have[a[i]] = 1;
  }
  cout << ans << endl;
  return 0;
}
