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>
#include <assert.h>

using namespace std;

int main()
{
  int n;
  cin >> n;
  map<int, int, greater<int>> a;
  for (int i = 0; i < n; i++)
  {
    int t;
    cin >> t;
    a[t]++;
  }
  int ans = 0;
  for (pair<int, int> i : a)
  {
    if (i.second < 1)
      continue;
    int bit = 1;
    while (bit < i.first)
      bit *= 2;
    if (bit == i.first)
      ans += i.second / 2;
    int c = min(i.second, a[bit - i.first]);
    ans += c;
    a[bit - i.first] -= c;
  }
  cout << ans << endl;

  return 0;
}
