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<map>
#include<algorithm>
using namespace std;
multiset<int> list;
int pow2[30];
int main(){
	int i,n,x,tot=0;
	for(i=1;i<=30;i++)pow2[i-1]=(1<<i);
	cin>>n;
	for(i=1;i<=n;i++)cin>>x,list.insert(x);
	while(!list.empty()){
		multiset<int>::iterator itr=list.end();
		itr--;
		x=*itr;
		list.erase(itr);
		int y=*upper_bound(pow2,pow2+30,x)-x;
		multiset<int>::iterator fin=list.find(y);
		if(fin==list.end())continue;
		list.erase(fin);
		tot++;
	}
	cout<<tot;
	return 0;
}
/*1
3
1 2 3
*/
/*2
5
3 11 14 5 13
*/