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 N;
multiset<long long> A;
int R;

int buddy(int x) {
  int p = 1;
  while(p <= x) p *= 2;
  return p - x;
}

int main() {
  cin >> N;
  for(int i = 0; i < N; ++i) {
    long long a; cin >> a; A.insert(a);
  }
  while(!A.empty()) {
    auto it = A.end(); --it;
    int x = *it; A.erase(it);
    int y = buddy(x);
    it = A.find(y);
    if(it != A.end()) {
      A.erase(it);
      ++R;
    }
  }
  cout << R << endl;
  return 0;
}
