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;

multiset <int> Set;
int n,ans=0;

int getpow(int x){
	int ret=1;
	while(ret<=x) ret+=ret;
	return ret;
}

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0); cout.tie(0);
	cin>>n;
	for(int i=0;i<n;i++){
		int x;
		cin>>x;
		Set.insert(x);
	}
	while(!Set.empty()){
		multiset <int> :: iterator it=Set.end();
		it--;
		int x=*it;
		int i=getpow(x);
		Set.erase(Set.find(x));
		if(Set.find(i-x)!=Set.end()){
			Set.erase(Set.find(i-x));
			ans++;
		}
	}
	cout<<ans<<endl;
	return 0;
}