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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;

namespace B
{
	class Program
	{
		static void Main(string[] args)
		{
			int N = int.Parse(Console.ReadLine());
			string[] input = Console.ReadLine().Split(' ');
			int[] A = new int[N];
			for(int i = 0; i<N; i++)
				A[i] = int.Parse(input[i]);

			int count = 0;
			for(int i=0; i<N-1; i++)
				for(int j=1; j<N && i<j; j++)
					if(((A[i] + A[j]) & (A[i]+A[j]-1)) == 0)
						count++;
			Console.WriteLine(count);
		}
	}
}