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<cstdio>
#include<algorithm>
#include<set>
using namespace std;
int n, res;
multiset<int>Set;
int main() {
	int i, a;
	scanf("%d", &n);
	for (i = 0; i < n; i++) {
		scanf("%d", &a);
		Set.insert(a);
	}
	while (!Set.empty()) {
		auto it = Set.end();
		it--;
		int x = *it;
		Set.erase(it);
		for (i = 1; i <= x; i *= 2);
		if (Set.find(i-x) != Set.end()) {
			Set.erase(Set.find(i - x));
			res++;
		}
	}
	printf("%d\n", res);
}