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>
#define rep(i,n) for ((i)=1;(i)<=(n);(i)++)
using namespace std;
int n,i,j,k,s,aa[200005],vis[200005];
int main()
{
	scanf("%d",&n);
	rep(i,n)
	{
		scanf("%d",&aa[i]);
	}
	sort(aa+1,aa+n+1);
	for (k=1073741824;k>=2;k/=2)
	{
		i=1;j=n;
		while (i<j)
		{
			while (vis[i]) i++;
			while (vis[j]) j--;
			if (i>=j) break;
			if (aa[i]+aa[j]==k)
			{
				vis[i]=vis[j]=1;
				s++;
				i++;
				j--;
				continue;
			}
			if (aa[i]+aa[j]<k) i++;
			else if (aa[i]+aa[j]>k) j--;
		}
	}
	cout<<s<<endl;
	return 0;
}