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 = readline.to_i
ai = readline.split.map(&:to_i).sort

T1 = Math.log2(ai[0]).ceil
T2 = Math.log2(ai[-1]).floor


def find_matching(a,counts)
  i = 0
  j = a.size-1
  while a[i] < 0 and a[j] > 0
    # pp "i,j,#{a[i]},#{a[j]}"
    if -a[i] == a[j]
      counts[i] += 1
      counts[j] += 1
      i += 1
      j -= 1
    elsif -a[i] > a[j]
      i += 1
    elsif -a[i] < a[j]
      j -= 1
    end
  end
end

# pp T1,T2,ai

counts = Array.new(N,0)
(T1..T2).each do |t|
  x = 2**t
  mapped = ai.map {|a| a-x }
  find_matching(mapped, counts)
  # pp "mapped", mapped, "counts:", counts
end

# pp counts
i = 0
num_matching = 0
while i < counts.size
  n = counts[i]
  num_a = 1
  while ai[i] == ai[i+1]
    i += 1
    n += counts[i]
    num_a += 1
  end
  i += 1
  num_matching += (num_a<=n) ? num_a : n
end

puts num_matching/2
# puts (counts.count {|x| x>0})/2