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>
#include <vector>

using namespace std;
multiset<long long> s;
vector<int> v;
int main(){
	int i,n,ans = 0;
	cin >> n;
	for(i=0;i<n;i++){
		int x; cin >> x;
		s.insert(x);
	}
	long long res = 1;
	for(i=0;i<35;i++){
		v.push_back(res);
		res *= 2;
	}
	while(s.size()){
		long long x = *s.rbegin();
		auto it = s.lower_bound(x);
		s.erase(it);
		for(i=(int)v.size()-1;i>=0;i--){
			if(s.count(v[i] - x)){
				auto ite = s.lower_bound(v[i] - x);
				ans++; s.erase(ite);
				break;
			}
		}
	}
	cout << ans << endl;
}