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<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<map>
#define ll long long
#define inf 20021225
#define mxn 200010
using namespace std;
ll a[mxn];int n;
map<ll,int> mp;
int main()
{
	int ans=0;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%lld",&a[i]);
	sort(a+1,a+n+1);
	for(int i=n;i;i--)
	{
		ll j;
		for(j=(1ll<<33);j>a[i];j>>=1ll)
			if(mp[j-a[i]])	break;
		if(j>a[i])	ans++,mp[j-a[i]]--;
		else mp[a[i]]++;
	}
	printf("%d\n",ans);
	return 0;
}