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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
#if DEBUG
            ReadLine();
#endif
        }

        void Solve(ConsoleInput cin)
        {
            List<long> pow_2 = new List<long>();
            for (int i = 1; true; i++)
            {
                long tmp = (long)Math.Pow(2, i);
                if (tmp <= 2000000000)
                {
                    pow_2.Add(tmp);
                }
                else
                {
                    break;
                }
            }


            long n = cin.ReadLong;
            long[] a = cin.ReadLongArray(n);


            Dictionary<long, List<long>> dic = new Dictionary<long, List<long>>();

            for (int i = 0; i < n; i++)
            {
                List<long> tmp = new List<long>();
                for (int j = 0; j < n; j++)
                {
                    if (i == j)
                    {
                        continue;
                    }

                    if (pow_2.Contains(a[i] + a[j]))
                    {
                        tmp.Add(j);
                    }

                }
                if (tmp.Count() > 0)
                {
                    dic.Add(i, tmp);
                }
            }

            List<long> order = dic.ToList().OrderBy(x => x.Value.Count()).Select(x => x.Key).ToList<long>();


            int result = 0;

            foreach (long i in order)
            {
                if (dic[i].Count() == 0)
                {
                    continue;
                }

                long p = dic[i][0];

                dic[i].Remove(p);


                foreach (KeyValuePair<long, List<long>> pair in dic)
                {
                    pair.Value.Remove(i);
                    pair.Value.Remove(p);
                }

                result++;
            }
            Console.WriteLine(result);
        }

        class ConsoleInput
        {
            private readonly System.IO.TextReader _stream;
            private char _separator = ' ';
            private Queue<string> inputStream;

            public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
            {
                this._separator = separator;
                this._stream = stream;
                inputStream = new Queue<string>();
            }

            public string Read
            {
                get
                {
                    if (inputStream.Count != 0) return inputStream.Dequeue();
                    string[] tmp = _stream.ReadLine().Split(_separator);
                    for (int i = 0; i < tmp.Length; ++i)
                        inputStream.Enqueue(tmp[i]);
                    return inputStream.Dequeue();
                }
            }

            public string ReadLine { get { return _stream.ReadLine(); } }
            public int ReadInt { get { return int.Parse(Read); } }
            public long ReadLong { get { return long.Parse(Read); } }
            public double ReadDouble { get { return double.Parse(Read); } }
            public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
            public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
            public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
        }
    }
}