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 <iostream>
#include <map>
using namespace std;

map<long, int> mp;
int main() {
	int N; long a; cin >> N;
	for(int i=0; i<N; ++i){
	    cin >> a;
	    ++mp[a];
	}
	int ans=0;
	auto itr=mp.end();
	while(itr!=mp.begin()){
	    --itr;
	    long sum=1;
	    while(sum<=itr->first) sum *= 2;
	    sum -= itr->first;
	    if(sum==itr->first){
	        ans += mp[sum]/2;
	    }
	    else{
	        ans += min(itr->second, mp[sum]);
	        mp[sum] -= min(itr->second, mp[sum]);
	    }
	}
	cout << ans << endl;
	return 0;
}
