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,ans;
multiset<int> s;

int main(){
	cin>>n;
	while(n--){
		int x;
		cin>>x;
		s.insert(x);
	}
	while(!s.empty()){
		int now=*s.rbegin();
		s.erase(prev(s.end()));
		for(int i=1;i<31;++i)
			if(s.count((1<<i)-now)){
				s.erase(s.find((1<<i)-now));
				++ans;
				break;
			}
	}
	cout<<ans<<endl;
	return 0;
}