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=gets.chomp.to_i
if n == 1
  puts 0
  exit
end
ary=gets.chomp.split(' ').map(&:to_i)
ary.sort!
a_s = ary.size
c = 0
pr = []
30.times do |i|
  i += 1
  j = 2**i
  o_n = ary.index { |a| a > j }
  if o_n.nil?
    break if ary[a_s-1] + ary[a_s-2] < j 
    tmp = ary
  else
    tmp = ary[0..o_n]
  end
  t_s = tmp.size
  tmp.each_with_index do |t, idx|
    r_t = t_s - idx
    r_t.times do |r|
      r += idx
      break if tmp[r] + t > j
      if tmp[r] + t == j && idx != r
        c += 1
        pr << [idx, r]
        break
      end
    end
  end
end