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)

def calc(k)
    i = 2
    while k > i
        i **= 2
    end
    i - k
end

n = gets.to_i
ns = gets.split.map(&:to_i).sort

hash = Hash.new(0)
ns.each do |i|
    hash[i] += 1
end

ans = 0

(n-1).downto(0) do |i|
    next if hash[ns[i]] <= 0
    hash[ns[i]] -= 1    
    pair = calc(ns[i])
    if hash[pair] > 0
        hash[pair] -= 1
        ans += 1
    end
end
puts ans