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 <cstdio>
#include <map>
#include <algorithm>
using namespace std;
const int N=200005;
int n;
int a[N];
int cur,ans;
map <int,int> p;
bool cmp(int x,int y)
{
	return x>y;
}
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		p[a[i]]++;
	}
	sort(a+1,a+n+1,cmp);
	cur=1<<30;
	for (int i=1;i<=n;i++)
	{
		while (cur>2*a[i])
			cur/=2;
		while (p[a[i]]&&((cur-a[i]==a[i]&&p[cur-a[i]]>=2)||(cur-a[i]!=a[i]&&p[cur-a[i]]>=1)))
		{
			ans++;
			p[a[i]]--;
			p[cur-a[i]]--;
		}
	}
	printf("%d\n",ans);
	return 0;
}