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<iostream>
#include<map>
#include<algorithm>
using namespace std;
map<int,int>M;
int n,A[1<<18],ans;
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)
	{
		cin>>A[i];
		M[A[i]]++;
	}
	sort(A,A+n,greater<int>());
	for(int i=0;i<n;i++)
	{
		if(M[A[i]]==0)continue;
		M[A[i]]--;
		int now=-A[i];
		for(int j=32;j--;)
		{
			if(!(now&1LL<<j))continue;
			now-=1LL<<j;
			if(__builtin_popcount(now+A[i])==1&&M[now]>0)
			{
				M[now]--;
				ans++;
				break;
			}
		}
	}
	cout<<ans<<endl;
}