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<algorithm>
#include<cmath>
#include<cstring>
#include<map>
using namespace std;
const int N=300010;
int n,a[N];
bool vis[N];
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>=0;i--)
	{
		int j=n,k=1;
		while (j>=1)
		{
			if (vis[j]) { j--;continue;}
			while (k<j)
			{
				if (a[j]+a[k]>(1<<i)) break;
				if (!vis[k]&&a[j]+a[k]==(1<<i)) { vis[j]=vis[k]=1;ans++;break;}
				k++;
			}
			j--;
		}
	}
	printf("%d\n",ans);
	return 0;
}

