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;
const int MAX=2e5+5;
int n,ans;
int a[MAX];
map<int,int> ma;
bool use[MAX];
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i)
	  scanf("%d",&a[i]),++ma[a[i]];
	sort(a+1,a+1+n);
	for(int i=31;i>=1;--i)
	  {
	  	for(int j=1;j<=n;++j)
	  	  if(ma[a[j]])
		  {
	  	  	int x=(1<<i)-a[j];
	  	  	if(x<=0) break;
	  	  	if(x!=a[j])
	  	  	{
	  	  		if(ma[x]) ++ans,--ma[x],--ma[a[j]];
			}
			else
			{
				if(ma[x]>=2) ++ans,ma[x]-=2;
			}
		  }
	  }
	return printf("%d",ans),0;
}
