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;
typedef long long ll;

int main() {
  int N;
  cin >> N;
  vector<int> A(N);
  vector<bool> used(N);
  multiset<int> B;
  for (int i = 0; i < N; i++) {
    cin >> A[i];
    B.insert(A[i]);
  }
  int ans = 0;
  while (!B.empty()) {
    int M = *B.rbegin();
    B.erase(B.find(M));

    auto it = B.find((1 << ((int)log2(M)) + 1) - M);
    if (it != B.end()) {
      ans++;
      B.erase(it);
    }
  }
  cout << ans << endl;
}