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 main() {
  int n;
  cin >> n;
  long long a[n];
  unordered_map<long long, int> mp;
  unordered_map<long long, int> mp2;
  unordered_map<long long, int> mp3;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    mp[a[i]]++;
  }
  for (int i = 0; i < n; i++) {
    for (long long j = 2; j < 1e12; j *= 2) {
      if (j - a[i] == a[i] && mp[a[i]] > 0) {
        mp2[j - a[i]]++;
      } else if (j - a[i] != a[i]) {
        mp3[j - a[i]]++;
      }
    }
  }
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    ans += (mp2[a[i]] / mp[a[i]]) * (mp[a[i]] - 1);
    ans += mp3[a[i]];
  }
  cout << ans / 2 << endl;
  return 0;
}
