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: Wrong Answer)



import java.util.Arrays;
import java.util.HashMap;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		long[] a = new long[n];

		for (int i = 0; i < n; i++) {
			a[i] = Long.parseLong(sc.next());
		}

		Arrays.sort(a);
		int ans = 0;
		HashMap<Long, Long> remove = new HashMap<Long, Long>();

		for (int i = n - 1; i >= 0; i--) {
			if (remove.containsKey(a[i]))
				continue;
			for (int j = 0; j < i; j++) {
				if (remove.containsKey(a[j]))
					continue;

				if (judge(a[i] + a[j])) {
					ans++;
					remove.put(a[i], a[i]);
					remove.put(a[j], a[j]);
				}
			}
		}

		System.out.println(ans);

	}

	static boolean judge(long sum) {
		if ((sum & (sum - 1)) == 0)
			return true;
		else
			return false;

	}

}