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<map>
#include<queue>
using namespace std;
map<int,int> m1;
priority_queue<int> q1;
int t[200005];
int check(int a){
	for(int i=0;;i++){
		if((1<<i)>a)return ((1<<i)-a);
	}
}
int main(){
	int n;
	int i,j,k;
	int a,b,c;
	int s=0;
	cin>>n;
	for(i=0;i<n;i++){
		cin>>t[i];
		m1[t[i]]++;
		q1.push(t[i]);
	}
	while(!q1.empty()){
		a=q1.top(),q1.pop();
		if(m1[a]==0)continue;
		m1[a]--;
		b=check(a);
		if(m1[b]>0)m1[b]--,s++;
	}
	cout<<s<<endl;
	return 0;
}
