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 = STDIN.gets.to_i
numbers = STDIN.gets.split(' ').map(&:to_i)

# 最大値とペアを組んでべき乗になる値は一意
# A1 <= A2 ... <= An
# x = An
# 2のべき乗になるようなyを選ぶ
# x < x + y <= 2x

numbers = numbers.sort.reverse
count = 0

loop do
  break if numbers.empty?

  max = numbers.shift

  pow = 0
  1.upto(30) do |i|
    if (2 ** i) > max
      pow = i
      break
    end
  end

  index = numbers.index(2 ** pow - max)
  # p '----'
  # p max, pow, index
  # p '----'
  if index
    numbers.delete_at(index)
    count += 1
  end
end

puts count