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 main() {
	int n;
	cin>>n;
	int temp,cnt=0;
	multiset<int> s;
	for(temp=0;temp<n;temp++) {
		int x;
		cin>>x;
		s.insert(x);
	}

	while(s.size()>1) {
		auto it=s.end();
		it--;
		int num=*it;
		s.erase(it);
		//cout<<num<<"\n";
		int cur=1;
		for(int temp=0;temp<31;temp++) {
			//cout<<cur<<"\n";
			if(s.find(cur-num)!=s.end()) {
				cnt++;
				s.erase(s.lower_bound(cur-num));
				break;
			}
			cur=cur*2;
		}
	}
	cout<<cnt<<"\n";

}