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;
long long t,n,a[200000+10],ans;
multiset <long long> st; 
int main(){
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>a[i];
		st.insert(a[i]);
	}
	sort(a,a+n);
	for(int i=n-1;i>=0;i--){
		if(st.find(a[i])!=st.end()){
			t=1;
			st.erase(st.find(a[i]));
			for(int j=0;j<40;j++){
				t*=2;
				if(st.find(t-a[i])!=st.end()){
					st.erase(st.find(t-a[i]));
					ans++;
					break;
				}
			}
		}
	}
	cout<<ans;
}

