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 dp[][];
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long a[] = new long[n];
        HashMap<Long,HashSet<Integer>> mapA = new HashMap<>();
        for (int i = 0;i < a.length;++i){
            a[i] = sc.nextLong();
            if(!mapA.containsKey(a[i]))mapA.put(a[i],new HashSet<>());
            mapA.get(a[i]).add(i);
        }
        HashMap<Integer,HashSet<Integer>> graph = new HashMap<>();
        for (int i = 0;i < a.length;++i){
            for (int j = 0;j <= 32;++j){
                long t = (2L << j) - a[i];
                if(mapA.containsKey(t)){
                    if(!graph.containsKey(i))graph.put(i, (HashSet<Integer>)mapA.get(t).clone());
                    else graph.get(i).addAll((HashSet<Integer>)mapA.get(t).clone());
                }
            }
        }
        for (int i:graph.keySet()){
            graph.get(i).remove(i);
        }
        ArrayList<Integer> keys = new ArrayList<>(graph.keySet());
        keys.sort((i1,i2) -> {
            int s1 = graph.get(i1).size();
            int s2 = graph.get(i2).size();
            return Integer.compare(s1, s2);
        });
        long c = 0;
        boolean[] flags = new boolean[n];
        for (int k:keys){
            if(flags[k])continue;
            HashSet<Integer> s = graph.get(k);
            for (int k2:s){
                if(flags[k2])continue;
                flags[k] = true;
                flags[k2] = true;
                ++c;
                break;
            }
        }
        System.out.println(c);
    }

}