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 <set>
#define llint long long

using namespace std;

llint n;
llint a[200005];
multiset<llint> S;

llint get(llint x)
{
	llint mul = 1;
	for(;x;x/=2) mul *= 2;
	return mul;
}

int main(void)
{
	cin >> n;
	for(int i = 1; i <= n; i++) cin >> a[i], S.insert(a[i]);
	
	llint ans = 0;
	while(S.size()){
		auto it = S.end(); it--;
		llint v = *it;
		S.erase(it);
		llint x = get(v);
		if(S.count(x-v)){
			ans++;
			S.erase(S.lower_bound(x-v));
		}
	}
	cout << ans << endl;
	
	return 0;
}