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 p(int x){
	int k=0;
	while(1){
		if(x==(1<<k))return x;
		else if(x<(1<<k))return (1<<k)-x;
		else k++;
	}
}

int main(){
	int N;
	cin >> N;
	vector<int> A(N);
	for(auto &i:A)cin >> i;
	
	sort(A.begin(),A.end());
	
	int ans=0;
	while(!A.empty()){
		auto last=A.end();
		last--;
		int x=*last;
		int y=p(x);
		A.erase(last);
		if(binary_search(A.begin(),A.end(),y)){
			ans++;
			auto it=lower_bound(A.begin(),A.end(),y);
			A.erase(it);
		}
	}
	cout << ans << endl;
	return 0;
}