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;
multiset<int>s;
int main(){
	int n; scanf("%d",&n);
	for(int i=1; i<=n; ++i){
		int x; scanf("%d",&x); s.insert(x);
	}
	int ans=0;
	for(int i=1; i<=n&&!s.empty(); ++i){
		int k=*(--s.end());
		s.erase(--s.end());
		for(int j=1; j<32; ++j)
			if(s.find((1<<j)-k)!=s.end()){
				++ans; s.erase(s.find((1<<j)-k)); break;
			}
	}
	printf("%d",ans);
	return 0;
}