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;
long long n,a[200200];
vector<long long> v;
map<int,int> m;
long long dd=0;
int bbb(int n)
{
	int s=1;
	while(true)
	{
		s*=2;
		if(s>n)
		  break;
	}
	return s;
}
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)
	{
		cin>>a[i];
		m[a[i]]++;
		if(a[i]>dd)
		  dd=a[i];
    }
    long long s=1,ans=0;
	sort(a,a+n);
	for(int i=n-1;i>=0;i--)
	{
		if(m[a[i]]<=0)continue;
		int x=a[i];
		int y=bbb(x)-x;
		if(m[y])
		{
			m[x]--;
			m[y]--;
			if(m[y]>=0)
			ans++;
		}
	}
	cout<<ans;
	return 0;
}