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.Scanner;

public class Main{
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int[] a=new int[n];
		int[] aflag=new int[n];
		for(int i=0;i<n;i++){
			a[i]=sc.nextInt();
			aflag[i] = 0;
		}
		Arrays.sort(a);
		int b = n;
		int c = n-1;
		int count = 0;
		for(int max = 1073741824;max>1;max = max/2) {
			for(int i=c;i>=0;i--) {
				//System.out.println(max);
				if(a[i] >= max) {
					continue;
				}
				if(aflag[i] == 1) {
					continue;
				}
				if(a[i] * 2 < max) {
					break;
				}
				for(int j=c;j>=0;j--) {
					if(a[j] > max / 2) {
						c = i;
						continue;
					}
					if(aflag[j] != 1) {
						if(a[i] + a[j] == max) {
							count++;
							aflag[i] = 1;
							aflag[j] = 1;
							break;
						}
					}
				}
			}
		}
		
		System.out.println(count);
	}
}