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[200001];
int b[200001];
map<int,int> f;
int main()
{
	int n,s=0,i,t;
	scanf("%d",&n);
	for(i=0;i<n;i++)
		scanf("%d",&a[i]);
	sort(a,a+n);
	for(i=0;i<n;i++)
	{
		t=1;
		while(t<=a[i])
			t*=2;
		b[i]=t-a[i];
	}
	for(i=0;i<n;i++)
		f[a[i]]++;
	for(i=n-1;i>=0;i--)
	{
		if(f[a[i]])
		{
			f[a[i]]--;
			if(f[b[i]])
			{
				f[b[i]]--;
				s++;
			}
		}
	}
	printf("%d",s);
	return 0;
}