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;
int n;
multiset<int>s;
int main(){
	ios::sync_with_stdio(false);
	cin >> n;
	for(int i=1; i<=n ;i++){
		int x;cin >> x;
		s.insert(x);
	}
	int ans=0;
	while(!s.empty()){
		multiset<int>::iterator it=s.end();
		--it;
		int cur=*it;
		s.erase(it);
		for(int i=30; i>=0 ;i--){
			auto it2=s.lower_bound((1<<i)-cur);
			if(it2!=s.end() && *it2==(1<<i)-cur){
				ans++;
				s.erase(it2);
				break;
			}
		}
	}
	cout << ans << endl;
}