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: Accepted)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		int n = int.Parse(Console.ReadLine());
		long[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
		Array.Sort(nums);
		long answer = 0;
		int first = 0;
		int second = n-1;
		long aimNum = 1073741824;
		bool[] used = new bool[n];
		for(int i = 0; i < n; i++) used[i] = false;
		
		while(true)
		{
			if(n == 1 || aimNum == 1) break;
			first = 0;
			second = n-1;
			while(true)
			{
				if(nums[first] + nums[second] == aimNum)
				{
					if((!used[first]) && (!used[second]))
					{
						answer++;
						used[first] = true;
						used[second] = true;
						first++;
						second--;
					}else if(!used[first])
					{
						second--;
					}else if(!used[second])
					{
						first++;
					}else
					{
						first++;
						second--;
					}
				}else
				{
					if(nums[first] + nums[second-1] < aimNum) first++;
					else second--;
				}
				
				if(first >= second) break;

			}
			aimNum /= 2;
		}
		
		Console.WriteLine(answer);
	}

}