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: Accepted)

n = gets.to_i
balls = gets.split(" ").map(&:to_i).sort{|a,b| b<=>a}

h = Hash.new(0)
balls.each do |b|
  h[b] += 1
end

count = 0

twos = []
(1..31).each do |i|
  twos.push(2**i)
end
twos.reverse!

balls.each do |ball|
  next if h[ball] < 1
  h[ball] -= 1
  twos.each do |t|
    break if t < ball
    if h[t - ball] > 0
      h[t - ball] -= 1
      count += 1
      next
    end
  end
end

puts count