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,a[300001];
int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin>>n;
	for(int i=0;i<n;i++)cin>>a[i];
	multiset<int> s(a,a+n);
	int ans=0;
	while(!s.empty())
	{
		int x=*s.rbegin();s.erase(--s.end());
		for(int i=(1<<30);i;i>>=1)
			if(s.count(i-x))
			{
				ans++;
				s.erase(s.find(i-x));
				break;
			}
	}
	cout<<ans<<'\n';
}
