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
/* Accepted. */
#include<iostream>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<set>
#include<cmath>
using namespace std;
#define MAXN 200006
int n;
multiset<int> S;
int main() {
	cin >> n;
	for( int i = 0 , t ; i < n ; ++ i ) scanf("%d",&t) , S.insert(t);
	int ans = 0;
	while( !S.empty() ) {
		auto it = S.end(); --it;
		int x =  * ( it );
		S.erase( it );
		int k = log2( x ) + 1;
		if( S.count( (1<<k) - x ) ) S.erase(S.find((1<<k) - x) ) , ++ans;
	}
	cout << ans;
}
