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 a[200005];
int main()
{
	int n,i,ans=0;
	scanf("%d",&n);
	for(i=0;i<n;i++)
		scanf("%d",&a[i]);
	sort(a,a+n);
	for(i=30;i>=1;i--)
	{
		int p=0;
		int q=n-1;
		while(p<q)
		{
			if(a[p]+a[q]==(1<<i))
			{
				ans++;
				a[p++]=0;
				a[q--]=0;
			}
			else if(a[p]+a[q]<(1<<i))
				p++;
			else 
				q--;
		}
    	int len=0;
    	for(p=0;p<n;p++)
		{
			if(a[p])
				a[len++]=a[p];
		}
		n=len;
	}
	printf("%d\n",ans);
	return 0;
}