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: Accepted)

N,*xs = `dd`.split.map(&:to_i)
xn = Hash.new(0)
xs.each{ |x| xn[x] = (xn[x] || 0) + 1 }
xs.sort!.reverse!
ans = 0
P = (0..xs[0].bit_length).map{ |b| 1 << b }
xs.each{ |x|
  next if xn[x] == 0
  xn[x] -= 1
  m = x.bit_length
  y = P[m] - x
  if xn[y] > 0
    ans += 1
    xn[P[m] - x] -= 1
  end
}
p ans