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 <algorithm>
#include <stdio.h>
#include <deque>
#include <set>
using namespace std;
using ll = long long;
ll next(ll x) {
	ll i = 1;
	for (; i <= x; i *= 2);
	return i;
}
int main() {
	ll n, t, p;
	scanf("%lld", &n);
	multiset<ll> a;
	for (int i = 0; i < n; i++)
		scanf("%lld", &t), a.emplace(t);

	ll c = 0;
	while (!a.empty()) {
		t = *(--a.end());
		p = next(t) - t;
		a.erase(--a.end());

		auto lower = a.lower_bound(p);
		if (lower != a.end() && *lower == p)
			c++, a.erase(lower);
	}
	printf("%lld\n", c);
}