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<algorithm>
#include<map>
using namespace std;
int n,a[200005],ans;
map<int,int>f;
int main()
{
	scanf("%d",&n);for(int i=1;i<=n;++i) {scanf("%d",&a[i]);f[a[i]]++;}
	sort(a+1,a+1+n);
	for(int i=n;i;--i) {
		if(!f[a[i]]) continue;
		for(int j=1;j<=30;++j) {
			if((1<<j)==a[i]+a[i]&&f[a[i]]>1) {f[a[i]]-=2;ans++;}
			else if((1<<j)>a[i]&&f[(1<<j)-a[i]]&&(1<<j)-a[i]<a[i]) {f[a[i]]--;f[(1<<j)-a[i]]--;ans++;}
			if((1<<j)>a[i]&&(1<<j)-a[i]<=a[i]) break;
		}
	}
	printf("%d\n",ans);
	return 0;
}