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(){
	int N;
	cin>>N;
	vector<int> A(N);
	map<int,int> mp;
	for(int i=0;i<N;i++){
		cin>>A[i];
		mp[A[i]]++;
	}
	sort(A.begin(),A.end(),greater<int>());
	int ans = 0;
	for(int i=0;i<N;i++){
		if(mp[A[i]]==0)continue;
		long long a = (long long)1;
		while(a<=A[i])a*=2;
		if(A[i]*2!=a){
			if(mp[A[i]]>0&&mp[a-A[i]]>0){
				mp[A[i]]--;
				mp[a-A[i]]--;
				ans++;
			}
		}
		else{
			if(mp[A[i]]>1){
				ans++;
				mp[A[i]]-=2;
			}
		}
	}
	
	cout<<ans<<endl;
	
	
	return 0;
}