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: Wrong Answer)

N = STDIN.gets.chomp.to_i
A = STDIN.gets.chomp.split(' ').map(&:to_i)

A.sort!

hash = {}
cnt = 0

A.each do |ai|
  hash[ai] ||= 0
  hash[ai] += 1
end

A.reverse_each do |ai|
  bits = ai.bit_length
  next_pow2 = 2 ** bits
  diff = next_pow2 - ai

  # puts hash
  # puts "#{ai}, next_p2:#{next_pow2}, diff:#{diff}"

  if hash.key?(diff) && hash[diff] > 0
    cnt += 1
    hash[diff] -= 1
  end
end

puts cnt