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
array = gets.split.map(&:to_i)
even = []
odd = []
exp = []
cnt = 0
array.map { |e|
  if e%2==0
    even << e
  else
    odd << e
  end
}

even.sort!.reverse!
odd.sort!.reverse!

exp_odd = []
exp_even = []

max = even[0]
x = 2
while x < max
  exp_even << x
  x = x*2
end
exp_even << x

even.size.times do |i|
  (i+1).upto(even.size) do |j|
    if even[j]==nil
      break
    end
    if exp_even.include?(even[i]+even[j])
      cnt += 1
      even.delete_at(j)
      break
    end
  end
end

max = odd[0]
x = 2
while x < max
  exp_odd << x
  x = x*2
end
exp_odd << x

odd.size.times do |i|
  (i+1).upto(odd.size) do |j|
    if odd[j]==nil
      break
    end
    #puts odd[i]
    #puts odd[j]
    #puts odd[i]+odd[j]
    #puts
    if exp_odd.include?(odd[i]+odd[j])
      cnt += 1
      odd.delete_at(j)
      break
    end
  end
end

puts cnt