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(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n;
	cin>>n;
	multiset<int,greater<int> > M;
	for(int i=1,x;i<=n;i++)
		cin>>x,M.insert(x);
	int ans = 0;
	while(M.size()){
		int x = *M.begin();
		M.erase(M.begin());
		int y = (1<<(32-__builtin_clz(x)))-x;
		if(M.count(y)){
			ans++;
			M.erase(M.find(y));
		}
	}
	cout<<ans<<endl;
}
