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.*;
import java.util.Map.*;

class Main{
	static Scanner s=new Scanner(System.in);
	public static void main(String[] $){
		int n=s.nextInt();
		TreeMap<Integer,Integer> m=new TreeMap<>();
		for(int i=0;i<n;++i)
			m.merge(Integer.parseInt(s.next()),1,Integer::sum);

		int r=0;
		while(!m.isEmpty()){
			Entry<Integer,Integer> e=m.pollLastEntry();
			
			if(Integer.bitCount(e.getKey())==1) {
				r+=e.getValue()/2;
				continue;
			}
			
			int q=(int)((Long.highestOneBit(e.getKey())<<1)-e.getKey());
			Integer f=m.get(q);
			if(f!=null){
				int v=Math.min(f,e.getValue());
				r+=v;
				if(f>v)
					m.merge(q,-v,Integer::sum);
				else
					m.remove(q);
			}
			
			//System.err.println(q);
			//System.err.println(m);
		}
		System.out.println(r);
	}
}
