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 <cstdio>
#include <algorithm>
#include <set>


int main() {
  std::multiset<int> set;
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; ++ i) {
    int x;
    scanf("%d", &x);
    set.emplace(x);
  }
  int result = 0;
  while (set.size() >= 2) {
    int x = *set.rbegin();
    set.erase(--set.end());
    int b = 1;
    while (b <= x) b <<= 1;
    int y = b - x;
    auto it = set.find(y);
    if (it != set.end())
      set.erase(it), ++ result;
  }
  printf("%d\n", result);
}
