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() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  multiset<int> st;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    st.insert(x);
  }
  int res = 0;
  while (!st.empty()) {
    int x = *st.rbegin();
    st.erase(--st.end());
    int y = 1; while (y < x) y += y;
    int z = (__builtin_popcount(x) == 1 ? x : y - x);
    if (st.count(z)) {
      st.erase(st.find(z));
      ++res;
    }
  }
  cout << res << '\n';
  return 0;
}
