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 intt long long 
using namespace std;
int read(){int k;scanf("%d",&k);return k;}
multiset<intt>S;
multiset<intt>::iterator it,it1;
intt flag=0,ans,n,x;
int main(){	
	n=read();
	for(int i=1;i<=n;i++)x=read(),S.insert(x);
	while(!S.empty()){	
		it=S.end();it--;
		flag=0;
		S.erase(it);
		for(int i=1;i<=31;i++){	
			intt v=(1<<i)-*it;
			it1=S.find(v);
			if(it1==S.end())continue;
			flag=1;
			S.erase(it1);ans++;
		}	
	}		
	cout<<ans<<endl;
	return 0;
}	