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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {
	public static void main (String[] args) {
		HashSet<Integer> set = new HashSet<>();
		int power = 2;
		for (int i = 0; i < 30; i++) {
			set.add(power);
			power *= 2;
		}
 		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		ArrayList<Integer> list = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			list.add(sc.nextInt());
		}
		Collections.sort(list);
		int idx = n - 1;
		int count = 0;
		while (idx > 0) {
			int x = list.get(idx);
			for (int i = idx - 1; i >= 0; i--) {
				if (set.contains(x + list.get(i))) {
					list.remove(idx);
					list.remove(i);
					idx--;
					count++;
					break;
				}
			}
			idx--;
		}
		System.out.println(count);
	}
}