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;
using System.Linq;
class Program{
	static void Main(){
		int n=int.Parse(Console.ReadLine());
		long[] a=Array.ConvertAll(Console.ReadLine().Split(),long.Parse);
		long ans=0,o=1;
		Array.Sort(a,ca);
		var hs=new Dictionary<long,int>();
		for(int i=0;i<n;i++){
			if(hs.ContainsKey(a[i])&&hs[a[i]]>0){
				ans++;
				continue;
			}
			for(int j=1;(o<<j)-a[i]<=a[i];j++){
				if((o<<j)>a[i]){
					if(hs.ContainsKey((o<<j)-a[i])){hs[(o<<j)-a[i]]++;}
					else{hs.Add((o<<j)-a[i],1);}
				}
			}
		}
		Console.WriteLine(ans);
	}
	static int ca(long a,long b){
		if(a<b){return 1;}
		else if(a>b){return -1;}
		else{return 0;}
	}
}