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 n,res;
multiset <int> Set;
int main() {
	int i,a;
	cin >> n;
	for(i = 0;i < n;i++) {
		cin >> a;
		Set.insert(a);
	}
	while(!Set.empty()) {
		multiset<int>::iterator it = Set.end();
		it--;
		int x = *it;
		Set.erase(it);
		for(i = 1;i <= x;i *= 2);
		if(Set.find(i-x) != Set.end()) {
			Set.erase(Set.find(i-x));
			res++;
		}
	}
	cout << res << endl;
	return 0;
}