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;
#define rep(i, n) for (int i = 0; i < n; i++)

int main()
{
  int N;
  cin >> N;
  multiset<int> ms;

  rep(i, N)
  {
    int a;
    cin >> a;
    ms.insert(a);
  }

  int ans = 0;

  while (!ms.empty())
  {
    auto it = --ms.end();
    int v = *it;
    ms.erase(it);

    int b = 1;
    while (b <= v)
      b *= 2;

    auto jt = ms.find(b - v);
    if (jt != ms.end())
    {
      ans++;
      ms.erase(jt);
    }
  }

  cout << ans << endl;
}
