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 <set>
#include <cstdio>
using namespace std;

const int N = 1 << 20;
int n;
int a[N];
multiset <int> st;

int main() {
	scanf("%d", &n);
	for (int i = 0; i < n; ++ i) {
		scanf("%d", &a[i]);
		st.insert(a[i]);
	}
	int ans = 0;
	while (!st.empty()) {
		int x = *st.rbegin();
		st.erase(-- st.end());
		for (int i = 30; i; -- i) {
			int y = (1 << i) - x;
			if (st.find(y) != st.end()) {
				multiset <int> :: iterator it = st.lower_bound(y);
				st.erase(it);
				++ ans;
				break;
			}
		}
	}
	printf("%d\n", ans);
	return 0;
}