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: Time Limit Exceeded)


DBG = !true
nl = "\n"

n = gets.to_i
a = gets.split.map{|x| x.to_i}
h = {}
for i in 0...a.size
  x = a[i]
  if h.keys.include?(x)
    h[x] += 1
  else
    h[x] = 1
  end
end

b = []
for k in h.keys
  b << [k, h[k]]
end
b.sort_by!{|x| x[0]}

puts "bsz: #{b.size}" if DBG
print b if DBG
puts "" if DBG

sum = 0
(b.size - 1).downto(0) { |i|
  c = b[i]
  key   = c[0]
  #card  = c[1]
  card  = h[key]

  # find msb
  msb = 2**32
  while (msb & key) == 0
    msb /= 2
  end

  bud = 2*msb - key
  print "i: #{i} ky:#{key} cd:#{card} msb:#{msb} bud:#{bud}#{nl}" if DBG

  next if !h.keys.include?(bud)
  if bud != key
    bcard = h[bud]
    npairs = [card, bcard].min
    sum += npairs
    h[bud] -= npairs
  else
    npairs = card/2
    sum += npairs
  end
}

print sum