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<cstdio>
#include<set>
#include<algorithm>
int N;
std::multiset<int>A;
int main(){
	scanf("%d",&N);
	for(int i=0,a;i<N;i++)scanf("%d",&a),A.insert(a);
	int ans=0;
	while(A.size()){
		int x=*A.rbegin(),y=1;
		A.erase(A.find(x));
		while(y<=x)y*=2;
		std::multiset<int>::iterator it=A.find(y-x);
		if(it!=A.end()){
			A.erase(it);
			ans++;
		}
	}
	printf("%d\n",ans);
}