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.to_i
as = gets.split.map(&:to_i)

mp = Hash.new(0)
as.each do |a|
    mp[a] += 1
end

ans = 0
mp.keys.sort.reverse.each do |a|
    30.downto(0) do |i|
        break if mp[a] == 0
        b = (1<<i) - a
        next if mp[b] == 0
        if a == b
            add = mp[a]/2
        else
            add = mp[a] < mp[b] ? mp[a] : mp[b]
        end
        ans += add
        mp[a] -= add
        mp[b] -= add
    end
end
puts ans