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;
inline void fast() { ios::sync_with_stdio(0), cin.tie(0), cout.tie(0); }
void solve() {
  int n;
  cin >> n;
  vector<long long> arr(n), power2(30);
  map<long long, long long> freq;
  long long i = 0, ans = 0;
  for (int i = 1; i <= 30; i++) power2[i - 1] = (1LL << i);
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    freq[arr[i]]++;
  }
  for (int i = 0; i < arr.size(); i++) {
    for (int j = 0; j < 30; j++) {
      long long temp = power2[j] - arr[i];
      if (!freq[temp])
        continue;
      else {
        ans += freq[temp];
        if (arr[i] == temp) ans--;
      }
    }
  }
  cout << ans / 2 << "\n";
}
int main(void) {
  fast;
  solve();
}
