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;

int main() {
  int n;
  cin >> n;
  multiset<long long> a;
  for (int i = 0; i < n; i++) {
    int num;
    cin >> num;
    a.insert(num);
  }

  int ans = 0;
  while (!a.empty()) {
    long long x = *a.rbegin();
    a.erase(a.find(x));
    long long next_two_power = 1;
    while (next_two_power <= x) {
      next_two_power <<= 1;
    }

    long long target = next_two_power - x;
    auto it = a.find(target);
    if (it != a.end()) {
      a.erase(it);
      ans++;
    }
  }
  cout << ans;
}
