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-csc 3.5.0) (judge verdict: Accepted)

/* author :: eSeF */
using System;
using System.Linq;
using System.Collections.Generic;
class AC
{
    static void Main()
    {
        int N = int.Parse(Console.ReadLine());
        var A = Console.ReadLine().Split().Select(long.Parse).ToArray();
        Array.Sort(A);
        Array.Reverse(A);
        var rec = new Dictionary<long, int>();
        for(var i = 0; i < N; i++)
        {
            if (rec.ContainsKey(A[i])) rec[A[i]]++;
            else rec[A[i]] = 1;
        }

        int ans = 0;
        for(var i = 0; i < N; i++)
        {
            if (rec[A[i]] == 0) continue;
            for(var j = 31; j >= 0; j--)
            {
                long now = (1L << j) - A[i];
                if (rec.ContainsKey(now))
                {
                    if (now == A[i] && rec[now] >= 2) 
                    {
                        ans++;
                        rec[now] -= 2;
                        break;
                    }
                    if (now != A[i] && rec[now] >= 1)
                    {
                        ans++;
                        rec[now]--;
                        rec[A[i]]--;
                        break;
                    }
                }
            }
        }
        Console.WriteLine(ans); 
    }
}
/* for input */
static class Csin
{
    public static string[] StrArray() => Console.ReadLine().Split();
    public static string[] StrArray(char separator) => Console.ReadLine().Split(separator);

    private static T Conv<T>(string value) => (T)Convert.ChangeType(value, typeof(T));
    public static (T, U) ReadTuple<T, U>(string[] input) => (Conv<T>(input[0]), Conv<U>(input[1]));
    public static (T, U, V) ReadTuple<T, U, V>(string[] input) => (Conv<T>(input[0]), Conv<U>(input[1]), Conv<V>(input[2]));
    public static (T, U, V, W) ReadTuple<T, U, V, W>(string[] input) => (Conv<T>(input[0]), Conv<U>(input[1]), Conv<V>(input[2]), Conv<W>(input[3]));
    public static (T, U, V, W, X) ReadTuple<T, U, V, W, X>(string[] input) => (Conv<T>(input[0]), Conv<U>(input[1]), Conv<V>(input[2]), Conv<W>(input[3]), Conv<X>(input[4]));

    public static (T, U) Input<T, U>() => ReadTuple<T, U>(StrArray());
    public static (T, U, V) Input<T, U, V>() => ReadTuple<T, U, V>(StrArray());
    public static (T, U, V, W) Input<T, U, V, W>() => ReadTuple<T, U, V, W>(StrArray());
    public static (T, U, V, W, X) Input<T, U, V, W, X>() => ReadTuple<T, U, V, W, X>(StrArray());
}