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.

Examples

Input

3
1 2 3


Output

1


Input

5
3 11 14 5 13


Output

2
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

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