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;
int n,ans;
int a[200105],b[200105];
map<int,int>cnt;
int main(){
	cin>>n;
	for(int i=1;i<=n;i++)cin>>a[i];
	for(int i=1;i<=n;i++)cnt[a[i]]++;
	sort(a+1,a+n+1);
	for(int i=1;i<=n;i++){
		b[i]=1;
		while(b[i]<=a[i])b[i]*=2;
		b[i]-=a[i];
	}
	for(int i=n;i>=1;i--){
		if(cnt[a[i]]){
			cnt[a[i]]--;
		    if(cnt[b[i]])cnt[b[i]]--,ans++;	
		}
	}
	cout<<ans<<endl;
	return 0;
}