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.chomp.split.map(&:to_i).sort
h = Hash.new(0)
a.each do |v|
    h[v] += 1
end

b = [1]
1.upto(32){|i| b[i] = b[i-1]<<1} 
b.reverse!

ans = 0

used = Hash.new(0)

a.each do |v|
    if used[v] > 0
        used[v] -= 1
        next
    end
    h[v] -= 1
    flag = 0
    b.each do |w|
        if h[w - v] > 0
            ans += 1
            h[w - v] -= 1
            used[w - v] += 1
            used[v] += 1
            flag = 1
            break
        end
    end
    h[v] += 1 if flag == 0
end
puts ans