#include<cstdio>
#include<iostream>
#include<map>
#include<algorithm>
using namespace std;
const int N=2e5+10;
int n,a[N],ans;
map<int,int>p;
int main(){
	scanf("%d",&n);
	for(register int i=1;i<=n;i++)scanf("%d",&a[i]),p[a[i]]++;
	sort(a+1,a+n+1);
	for(register int i=n;i;i--)
		if(p[a[i]]>0){
			int x=1;
			while(x<=a[i])x<<=1;
			int b=x-a[i];
			if(p.count(b)&&(p[b]>(a[i]==b)))p[b]--,p[a[i]]--,ans++;
		}
	printf("%d\n",ans);
	return 0;
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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

### Response

```cpp
#include<cstdio>
#include<iostream>
#include<map>
#include<algorithm>
using namespace std;
const int N=2e5+10;
int n,a[N],ans;
map<int,int>p;
int main(){
	scanf("%d",&n);
	for(register int i=1;i<=n;i++)scanf("%d",&a[i]),p[a[i]]++;
	sort(a+1,a+n+1);
	for(register int i=n;i;i--)
		if(p[a[i]]>0){
			int x=1;
			while(x<=a[i])x<<=1;
			int b=x-a[i];
			if(p.count(b)&&(p[b]>(a[i]==b)))p[b]--,p[a[i]]--,ans++;
		}
	printf("%d\n",ans);
	return 0;
}
```