#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<map>
#define N 200005
using namespace std;
int n,a[N],ans;
map<int,int> s;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]),s[a[i]]++;
	sort(a+1,a+1+n);
	for(int i=n;i;i--)
		if(s[a[i]]>0){
			int t=(1<<((int)log2(a[i])+1))-a[i];
			if((a[i]!=t && s[t]>0) || (a[i]==t && s[t]>1)){
				ans++;
				s[a[i]]--;
				s[t]--;
			}
		}
	printf("%d\n",ans);
	return 0;
}
### Prompt

Your challenge is to write a Cpp solution to the following problem:

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<iostream>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<map>
#define N 200005
using namespace std;
int n,a[N],ans;
map<int,int> s;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]),s[a[i]]++;
	sort(a+1,a+1+n);
	for(int i=n;i;i--)
		if(s[a[i]]>0){
			int t=(1<<((int)log2(a[i])+1))-a[i];
			if((a[i]!=t && s[t]>0) || (a[i]==t && s[t]>1)){
				ans++;
				s[a[i]]--;
				s[t]--;
			}
		}
	printf("%d\n",ans);
	return 0;
}
```