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)


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

print h if DBG

for x in h.keys
  for t in 0..31
    y = 2**t - x
    if x == y
      h[x][1] = true
    elsif h.keys.include?(y)
      h[x][2] << y
    end
  end
end

puts "----" if DBG
print h if DBG
puts "----" if DBG

slf = 0
pairs = 0
for x in h.keys
  print h[x][2] if DBG
  puts "====" if DBG
  pairslocal = h[x][2].empty? ? 0 :
       h[x][2].map{|y| h[y][0]}.inject(:+)
  if pairslocal > h[x][0]
    pairslocal = h[x][0]
  end
  printf("pl:%d\n", pairslocal) if DBG
  pairs += [pairslocal, h[x][0]].min
  rest = h[x][0] - pairslocal
  slf += rest / 2
end

print slf + pairs/2