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<map>
#include<cstdio>
#include<vector>
#include<algorithm>
using namespace std;
const int MAXN=200005;
map<int,int>T;
int n,a[MAXN],ans;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%d",&a[i]),T[a[i]]++;
	sort(a+1,a+n+1);
	for(int i=1<<30;i>=1;i>>=1)
		for(int j=1;j<=n&&a[j]<i;j++)
			if(T[a[j]]&&T[i-a[j]]){
				if(T[a[j]]==1&&i==a[j]*2)
					continue;
				T[a[j]]--,T[i-a[j]]--,ans++;
			}
	printf("%d\n",ans);
}
