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;
int x[200000];
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)
	{
		cin>>x[i];
	}
	sort(x,x+n);
	int ans=0;
	for(int h=(1<<30);h>0;h>>=1)
	{
		for(int i=0,j=n-1;i<j;i++)
		{
			if(x[i]!=-1)
			{
				while(j>i and (x[j]==-1 or x[i]+x[j]>h))
				{
					j--;
				}
				if(j>i and x[j]!=-1 and x[i]+x[j]==h)
				{
					ans++;
					x[i]=x[j]=-1;
				}
			}
		}
	}
	cout<<ans;
	return 0;
}