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.Scanner;
public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = Integer.parseInt(sc.next());
		long[] a = new long[N];
		for(int i=0;i<N;i++)a[i]=Long.parseLong(sc.next());
		Arrays.sort(a);

		HashMap<Long,Integer> map=new HashMap<>();
		
		for(int i=0;i<N;i++){
			if(map.containsKey(a[i])) {
				map.put(a[i],1+map.get(a[i]));
			}else {
				map.put(a[i],1);
			}
		}

		long res = 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){
				res++;
				map.put(diff,map.get(diff)-1);
			}
		}
		System.out.println(res);

	}

}