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 fre(x) freopen(#x".in","r",stdin);freopen(#x".out","w",stdout)
using namespace std;
int n,ans;
multiset<int>st;
int main()
{
//	fre(powers);
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		int x;
		scanf("%d",&x);
		st.insert(x);
	}
	while(!st.empty())
	{
		multiset<int>::iterator it=st.end();
		it--;
		int x=*it;
		st.erase(it);
		int y=1;
		while(y<=x) y<<=1;
		if(st.find(y-x)!=st.end())
		{
			st.erase(st.find(y-x));
			ans++;
		}
	}
	printf("%d\n",ans);
}
/*
4
3 5 11 13
*/