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
#include <bits/stdc++.h>
using namespace std;

int n;
map <int, int> a;
int ans;

int main()
{
	cin >> n;
	while (n--){
		int x;
		cin >> x;
		a[x]++;
	}
	
	while (!a.empty()){
		map <int, int> :: iterator it=a.end();
		it--;
		int x=it->first;
		
		if (!a[x])  throw;
			
		a[x]--;
		if (!a[x])  a.erase (x);
		
		int z=1;
		while (z <= x)
			z <<= 1;
			
		if (a.count (z-x) > 0){
			a[z-x]--;
			if (!a[z-x])
				a.erase (z-x);
				
			ans++;
		}
	}
	
	cout << ans << endl;
	return 0;
}