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;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		string[] str = Console.ReadLine().Split();
		int[] A = new int[N];
		var dic = new Dictionary<int,int>();
		int ans = 0;
		for(var i=0;i<N;i++){
			A[i] = int.Parse(str[i]);
			if(dic.ContainsKey(A[i])){
				dic[A[i]] += 1;
			} else {
				dic[A[i]] = 1;
			}
		}
		for(var i=0;i<N;i++){
			for(var j=1;j<=32;j++){
				int a = (int)Math.Pow(2,j);
				if(dic.ContainsKey(a-A[i])){
					if(a==A[i]){
						if(dic[A[i]] >= 2){
							ans += 1;
							dic[A[i]] -= 2;
						}
					} else {
						ans += 1;
						dic[A[i]] -= 1;
						dic[a-A[i]] -= 1;
					}
					break;
				}
			}
		}
		Console.WriteLine(ans/2);
	}
}