Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.

Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Constraints

* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Examples

Input

3
1 2 3


Output

1


Input

5
3 11 14 5 13


Output

2
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

int main() {
  int N;
  cin >> N;
  vector<int> A(N);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
  }

  int ans = 0;
  multiset<int, greater<int>> s(begin(A), end(A));
  while(!s.empty()) {
    int mx = *s.begin();
    s.erase(s.begin());
    
    int cnt = 0;
    for (int tmp = mx; tmp > 0; tmp >>= 1) cnt++;
    
    int base = 1 << cnt;

    auto it = s.find(base - mx);
    if (it != s.end()) {
      s.erase(it);
      ans++;
    }
  }

  cout << ans << endl;
}
