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;
const int N=2e5+5;
multiset<int>w;
int n,a[N],two[N],ans;
int main(){
	ios::sync_with_stdio(false);
	cin>>n;for(int i=1;i<=n;++i)cin>>a[i];
	two[0]=1;for(int i=1;i<32;++i)two[i]=two[i-1]<<1;
	sort(a+1,a+1+n);for(int i=1;i<=n;++i)w.insert(a[i]);
	while(!w.empty()){
		int x=*w.rbegin();w.erase(w.lower_bound(x));
		for(int j=31;j;--j){
			if(w.count(two[j]-x)){
				++ans;w.erase(w.lower_bound(two[j]-x));
				break;
			}
		}
	}cout<<ans<<endl;return 0;
}