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: Accepted)

import java.util.Scanner;
import java.util.TreeMap;

class Main {
    private static Scanner scan = new Scanner(System.in);

    public static void main(String[] args) {
       int n = scan.nextInt();
       int[] ar = new int[n];
        for (int i = 0; i < n; i++) {
            ar[i] = scan.nextInt();
        }

        TreeMap<Integer,Integer> ax = new TreeMap<>();

        for (int i = 0; i < ar.length; i++) {
            Integer x = ax.get(ar[i]);
            ax.put(ar[i],x==null?1:x+1);
        }

        int result = 0;
       while (!ax.isEmpty()){
            Integer cur = ax.lastKey();
            if(ax.get(cur) == 1){
                ax.remove(cur);
            }else{
                ax.put(cur,ax.get(cur)-1);
            }

            int pos = 1;
            while (pos <= cur) pos*=2;
            int need = pos-cur;
            Integer got = ax.get(need);
            if(got == null){
                continue;
            }
            result++;
            if(got == 1){
                ax.remove(need);
            }else{
                ax.put(need,got-1);
            }
       }

        System.out.println(result);
    }
}