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[200010];
bool used[200010];
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
	}
	sort(a+1,a+n+1);
	int ans=0;
	for (int i=30;i;i--)
	{
		for (int j=1,k=n;j<=n;j++)
		{
			if (used[j])
			{
				continue;
			}
			while (k && (used[k] || a[j]+a[k]>(1<<i)))
			{
				k--;
			}
			if (j>=k)
			{
				break;
			}
			if (a[j]+a[k]==(1<<i))
			{
				used[j]=used[k]=true;
				ans++;
			}
		}
	}
	cout<<ans<<endl;
	return 0;
}
