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 B = 32;
long long P[B];
void init() {
  P[0] = 1;
  for (int i = 1; i < B; i++) P[i] = P[i - 1] * 2;
}
int main() {
  init();
  int n;
  cin >> n;
  int arr[n];
  for (int i = 0; i < n; i++) cin >> arr[i];
  long long ans = 0;
  for (int i = 1; i < B; i++) {
    unordered_map<long long, int> cnt;
    for (int j = 0; j < n; j++) {
      ans += cnt[P[i] - arr[j]];
      cnt[arr[j]]++;
    }
  }
  cout << ans << "\n";
  return 0;
}
