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; 

const int maxn=2e5+1e2;
const int maxm=2e9;
map <int,int> mp;

int a[maxn],cur[maxn]={0},num[maxn],link[maxn];

int cmp(int a,int b)
{
	return a>b;
}

int main()
{
	int n,ans=0;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&a[i]);
	sort(a+1,a+n+1,cmp);
	for(int i=1;i<=n;i++)
	{
		bool flag=false;
		for(int j=30;j>=1;j--)
		{
			if(mp[(1<<j)-a[i]]>0)
			{
				mp[(1<<j)-a[i]]--;
				ans++;
				flag=true;
				break;
			}
		}
		if(!flag)mp[a[i]]++;
	}
	printf("%d\n",ans);
	return 0;
}