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;

const int N = 2e5 + 8;
long long a[N] , n , x , cnt , t;
multiset<long long> s;

int main()
{
	cin >> n;
	for(int i = 0 ; i < n ; i++)
	{
		cin >> a[i];
		s.insert(a[i]);
	}
	sort(a , a + n);
	for(int i = n - 1 ; i >= 0 ; i--)
	{
		t = 1;
		if(s.find(a[i]) != s.end())
		{
			s.erase(s.find(a[i]));
			for(int j = 0 ; j < 40 ; j++)
			{
				t *= 2;
				if(s.find(t - a[i]) != s.end())
				{
					cnt++;
					s.erase(s.find(t - a[i]));
					break;
				}
			}
		}
	}
	cout << cnt;
}