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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

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

public class Main {

	static int n, a[];
	static boolean known[];
	
	public static long solve() {
		long ans = 0;
		
		for(int i = n - 1; i >= 0; --i) {
			int key = (int)(Math.log(a[i]) / Math.log(2)) + 1;
			key = (int)Math.pow(2,  key) - a[i];
			int tmp = Arrays.binarySearch(a, key);
			if(tmp >= 0 && tmp != i && known[tmp] != true) {
				ans++;
				known[tmp] = true;
			}
		}
		
		return ans;

	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		n = sc.nextInt();
		a = new int[n];
		known = new boolean[n];
		for (int i = 0; i < n; ++i) {
			a[i] = sc.nextInt();
		}
		sc.close();
		
		Arrays.sort(a);
		
		long ans = solve();
		System.out.println(ans);
	}

}