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 n,ans=0;
map<int,int> mp;
int main(){
	cin>>n;
	int t;
	for(int i=0;i<n;i++){
		cin>>t;
		mp[t]++;
	}
	map<int,int>::iterator it=mp.begin();
	while(!mp.empty()){
		it=mp.end();
		it--;
		int x=it->first;
		if(mp[x]==0){
			throw;
		}
		mp[x]--;
		if(mp[x]==0){
			mp.erase(x);
		}
		int z=1;
		while(z<=x){
			z<<=1;
		}
		if(mp.count(z-x)>0){
			mp[z-x]--;
			if(mp[z-x]==0){
				mp.erase(z-x);
			}
			ans++;
		}
		
	}
	cout<<ans;
	return 0;
} 