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.to_i
a = gets.split.map(&:to_i)
b = Hash.new(0)
a.each do |num|
    b[num] += 1
end
ans = 0
i = 32
b.keys.sort.reverse.each do |num|
    p = b[num]
    next if p == 0
    i.downto(1) do |j|
        q = b[2**j-num]
        next if q == 0
        r = (p < q ? p : q)
        if num*2 == 2**j
            r /= 2
        end
        ans += r
        p -= r
        b[2**j-num] -= r
        i = j
    end
end
puts ans