#include<bits/stdc++.h>
using namespace std;

#define ll long long
int n, x, ans=0;
multiset<int> s;

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	
	cin >> n;
	for(int i=0;i<n;i++) {
		cin >> x;
		s.insert(x);
	}	

	for(int i=0;i<n && s.size();i++) {
		int e = *(--s.end());
		s.erase(--s.end());
		for(int j=0;j<32;j++) {
			if(s.find((1<<j) - e) != s.end()) {
				ans++;
				s.erase(s.find((1<<j) - e));
				break;
			}
		}
	}
	cout << ans;
}
### Prompt

Develop a solution in cpp 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<bits/stdc++.h>
using namespace std;

#define ll long long
int n, x, ans=0;
multiset<int> s;

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	
	cin >> n;
	for(int i=0;i<n;i++) {
		cin >> x;
		s.insert(x);
	}	

	for(int i=0;i<n && s.size();i++) {
		int e = *(--s.end());
		s.erase(--s.end());
		for(int j=0;j<32;j++) {
			if(s.find((1<<j) - e) != s.end()) {
				ans++;
				s.erase(s.find((1<<j) - e));
				break;
			}
		}
	}
	cout << ans;
}
```