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 <set>
using namespace std;
multiset <int> mp;
int main(){
	int n;
	cin >> n;
	for (int i = 1; i <= n; ++ i){
		int x;
		cin >> x;
		mp.insert(x);
	}
	int ans = 0;
	while (! mp.empty()){
		int x = *mp.rbegin();
		mp.erase(-- mp.end());
		for (int i = 30; i >= 0; -- i){
			int sum = 1 << i;
			if (mp.find(sum - x) != mp.end()){
				++ ans;
				mp.erase(mp.find(sum - x));
				break;
			}
		}
	}
	cout << ans << endl;
}
