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.*;

public class Main{
    
    static int[] v,d,c,result,used;
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        
        int n = Integer.parseInt(sc.next());
        Integer[] a = new Integer[n];
        Map<Integer,Integer> map = new TreeMap<>();
        
        ArrayList<Integer> nibeki = new ArrayList<>();
        for(long i=2; i<2_000_000_000; i*=2){
            nibeki.add((int)i);
        }
        
        for(int i=0; i<n; i++){
            a[i] = Integer.parseInt(sc.next());
        }
        Arrays.sort(a, Comparator.reverseOrder());
        int ans = 0;
        for(int i=0; i<n; i++){
            for(int j=0; j<nibeki.size(); j++){
                if(map.get(nibeki.get(j)-a[i])!=null
                    && map.get(nibeki.get(j)-a[i])>=1){
                    map.merge(a[i], -1, Integer::sum);
                    map.merge(nibeki.get(j)-a[i], -1, Integer::sum);
                    ans++;
                }
            }
            map.merge(a[i], 1, Integer::sum);
            
        }
        System.out.println(ans);
    }
}