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;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
namespace AtCoder
{
    class AC
    {
        const int mod = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        static readonly int[] dx = { 0, 1, 0, -1 };
        static readonly int[] dy = { 1, 0, -1, 0 };
        

        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            int N = int.Parse(Console.ReadLine());
            var A = cin.SplitReadL().ToList();
            A.Sort();
            A.Reverse();

            long ans = 0;
            bool[] x = new bool[N];
            Initialize(ref x, false);

            for(var i = 0; i < N; i++)
            {
                int k = Convert.ToString(A[i], 2).Length;
                long s = (1 << k);
                int r = LowerBound(A, s - A[i], x);
                
                if (r == -1 || r == N )
                {
                    continue;
                }
                //Console.WriteLine($"{s} {i},{A[i]} {r},{A[r]}");
                if (A[r] != s - A[i] || r == i) { continue; }

                ans++;
                x[r] = true;
                x[i] = true;
            }

            

            Console.WriteLine(ans);



            //Console.Out.Flush();
        }
        static public int LowerBound(List<long> list, long s, bool[]x)
        {
            int l = -1;
            int r = list.Count();

            while (r - l > 1)
            {
                int c = (l + r) / 2;
                if (list[c] > s || x[c])  
                {
                    l = c;
                }
                else 
                {
                    r = c;
                }
            }

            return r;
        }



    }
    public class Scanner
    {
        public int[] SplitRead()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReadL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }

    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
    }
}