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;

multiset<int> PQ;

int N, Ans;

int main() {
	ios::sync_with_stdio(false);

	cin >> N;
	for(int i = 0, c; i < N; i++) {
		cin >> c;
		PQ.insert(c);
	}

	for(int c; !PQ.empty();) {
		c = *prev(PQ.end());
		PQ.erase(prev(PQ.end()));
		for(int j = 1, t; j <= 31; j++) {
			t = (1ll<<j) - c;
			auto it = PQ.find(t);
			if(PQ.end() == it) continue;
			PQ.erase(it);
			Ans++;
			break;
		}
	}

	cout << Ans << endl;
	return 0;
}