Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3
1 2 3

Sample Output 1

1

We can form one pair whose sum of the written numbers is 4 by pairing the first and third balls.
Note that we cannot pair the second ball with itself.

Sample Input 2

5
3 11 14 5 13

Sample Output 2

2

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n = gets.to_i
numbers = gets.split(" ").map(&:to_i)
numbers.sort!.reverse!
count = 0
numbers.length.times do |index|
  numbers.length.times do |index2|
    if index == index2
      next
    end
    if (numbers[index] + numbers[index2]) & (numbers[index] + numbers[index2] - 1) == 0 && numbers[index] != 0 && numbers[index2] != 0
      count += 1
      numbers[index] = 0
      numbers[index2] = 0
    end
  end
end
puts count