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.chomp.to_i
a = gets.chomp.split(' ').map(&:to_i).sort

c = {}
n.times do |i|
  if c[a[i]]
    c[a[i]] += 1
  else
    c[a[i]] = 1
  end
end

answer = 0
(n - 1).downto(0) do |i|
  next if c[a[i]] <= 0
  c[a[i]] -= 1
  l = a[i].to_s(2).length
  t = (1 << l) - a[i]
  if c[t] && c[t] > 0
    c[t] -= 1
    answer += 1
  end
end
puts answer