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;
map<int,int>vis;
int n,ans,k,a[200005];
int tmp[50];
int main()
{
	tmp[0]=1;
	for (int i=1;i<=30;i++) tmp[i]=tmp[i-1]<<1;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		vis[a[i]]++;
	}
	sort(a+1,a+n+1);
	for(int i=n;i>=1;i--)
	{
		int pos=upper_bound(tmp,tmp+30,a[i])-tmp;
		if(pos>=31||!vis[a[i]]) continue;
		k=tmp[pos]-a[i];
		if((k!=a[i]&&vis[k])||(k==a[i]&&vis[k]>1))
		{
			ans++;
			vis[k]--;
		}
		vis[a[i]]--;
	}
	printf("%d\n",ans);
	return 0;
}