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() {
  vector<int> v;
  int s = 1;
  while (s <= 1e9) {
    s *= 2;
    v.push_back(s);
  }
  int n;
  cin >> n;
  multiset<long long> ms;
  set<long long> e;
  for (int i = 0; i < n; i++) {
    long long a;
    cin >> a;
    ms.insert(a);
    e.insert(a);
  }
  long long ans = 0;
  for (auto u : e) {
    for (int i = 0; i < v.size(); i++) {
      long long tmp = ms.count(v[i] - u);
      if (v[i] - u == u) {
        ans += (tmp * (tmp - 1));
        continue;
      }
      ans += tmp * ms.count(u);
    }
  }
  cout << ans / 2 << endl;
  return 0;
}
