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;
typedef long long ll;
const int maxn=2e5+5;
int n;
int a[maxn];
map<int,int>m;
int ans;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	sort(a+1,a+1+n);
	reverse(a+1,a+1+n);
	for(int i=1;i<=n;i++){
		if(m[a[i]]>0) m[a[i]]--,ans++;
		else{
			int tmp=(1<<(32-__builtin_clz(a[i])));
		//	cout<<tmp<<endl;
			m[tmp-a[i]]++;
		} 
	}
	printf("%d\n",ans);
	return 0;
}