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.Scanner;
import java.util.TreeMap;

public class Main {

	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		int n =sc.nextInt();
		TreeMap<Integer, Integer>map = new TreeMap<>();
		
		int tmp = 0;
		
		for (int i=0;i<n;i++) {
			int x = sc.nextInt();
			if (!map.containsKey(x)) {
				map.put(x, 0);
			}
			tmp = map.get(x);
			map.put(x, tmp+1);
		}
		int count = 0;
		while(!map.isEmpty()) {
			int a = map.lastKey();
			int b =Integer.highestOneBit(a)*2-a;
			if (map.containsKey(b) && a!=b) {
				count++;
				
				tmp = map.get(a);
				if (tmp>1) {
					map.put(a, tmp-1);
				} else {
					map.remove(a);
				}
				
				tmp = map.get(b);
				if (tmp>1) {
					map.put(b, tmp-1);
				} else {
					map.remove(b);
				}
			} else if (map.containsKey(b) && a==b) {
				tmp = map.get(a);
				if (tmp>=2) {
					count++;
				}
				
				if (tmp>2) {
					map.put(a, tmp-2);
				} else {
					map.remove(a);
				}
				
			} else {
				map.remove(a);
			}
		}
		System.out.println(count);
	}
}
