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>
#define lsb(x) ((x) & -(x))
using namespace std;

multiset <int> s;

int main()
{
	int n;
	cin >> n;
	vector <int> v(n);

	for (auto & i : v)
		cin >> i;

	sort(v.rbegin(), v.rend());

	int ans = 0;

	for (auto i : v) {
		bool ok = 0;
		for (long long p = 1; p <= 2000000000; p *= 2) {
			if (p >= i && s.find(p - i) != s.end()) {
				s.erase(s.find(p - i));
				ans++;
				ok = 1;
				break;
			}
		}
		if (!ok)
			s.insert(i);
	}

	cout << ans << '\n';

	return 0;
}
