#include<iostream>
#include<algorithm>
#include<map>
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);
	for(int i=n;i--;)
		if(M[a[i]]-->0)
			for(int j=32;1L<<j>a[i];j--)
				if(M[(1<<j)-a[i]]-->0){ans++;break;}
	cout<<ans<<endl;
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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

### Response

```cpp
#include<iostream>
#include<algorithm>
#include<map>
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);
	for(int i=n;i--;)
		if(M[a[i]]-->0)
			for(int j=32;1L<<j>a[i];j--)
				if(M[(1<<j)-a[i]]-->0){ans++;break;}
	cout<<ans<<endl;
}
```