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

typedef long long ll;
ll n, s, x;
multiset<ll> v;
int main()
{
	ll i, t;
	multiset<ll>::iterator it;
	cin >> n;
	for (i = 0; i < n; i++) {
		scanf ("%lld", &t);
		v.insert(t);
	}
	while (!v.empty()) {
		x = *v.rbegin();
		v.erase(v.find(x));
		for (i = 1; i <= x; i *= 2);
		it = v.find(i - x);
		if (it != v.end()) {
			s++;
			v.erase(it);
		}
	}
	cout << s;
    return 0;
}
