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>
using namespace std;

int main()
{
	int n;
	cin >> n;
	vector<int64_t> as(n);
	for (auto &a : as)
	{
		cin >> a;
	}
	multiset<int64_t> st;
	for (auto &a : as)
	{
		st.insert(a);
	}
	sort(as.begin(), as.end());
	reverse(as.begin(), as.end());
	int64_t ans = 0;
	for (auto &a : as)
	{
		if (st.find(a) != st.end())
		{
			st.erase(st.find(a));
			int64_t x = (1LL << (32 - __builtin_clz(a))) - a;
			auto itr = st.find(x);
			if (itr != st.end())
			{
				st.erase(itr);
				ans++;
			}
		}
	}
	cout << ans << endl;
	return 0;
}