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>
#define REP(i,n) for(int i=0;i<(n);++i)
#define ALL(v) (v).begin(),(v).end()
#define INF 1e9
typedef long long llong;
using namespace std;

int main(){
	int n;
	cin>>n;
	vector<int> a(n);//mmm.
	REP(i,n) cin>>a[i];
	sort(ALL(a));
	
	int cnt=0;
	while(a.size()>1){
		int want=1;
		while(want<=*(a.end()-1)) want*=2;
		want-=*(a.end()-1);
		
		auto itr=lower_bound(ALL(a),want);//二分探索.
		if(a.begin()<=itr&&itr<a.end()-1&&*(itr)==want){
			cnt++;
			a.erase(itr);
		}
		
		a.erase(a.end()-1);
	}
	
	cout<<cnt<<endl;
}//解答解説参考.