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.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;
import java.util.function.LongConsumer;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = sc.nextLong();
        Arrays.sort(a);

        Map<Long, Integer> map = new HashMap<>();
        for (Long l : a) map.put(l, map.getOrDefault(l, 0) + 1);

        long ans = 0;
        LongConsumer mapDec = l -> map.put(l, map.get(l) - 1);
        for (int i = n - 1; i >= 0; i--) {
            if (map.get(a[i]) == 0) continue;
            mapDec.accept(a[i]);
            long diff = 2 * Long.highestOneBit(a[i]) - a[i];
            if (map.containsKey(diff) && map.get(diff) > 0) {
                ans++;
                mapDec.accept(diff);
            }
        }
        System.out.println(ans);
    }
}