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;
typedef long long LL;

int main(){
	int n;
	cin >> n;
	map<int,int> r;
	for(int i = 0; i < n; i++){
		int k;
		cin >> k;
		r[k]++;
	}
	int ans = 0;
	while(!r.empty()){
		if(r.rbegin()->second == 0){
			r.erase(r.rbegin()->first);
			continue;
		}
		int f = r.rbegin()->first;
		r[f]--;
		int q = 1;
		while(q <= f) q *= 2;
		if(r.count(q-f) && r[q-f] > 0){
			r[q-f]--;
			ans++;
		}
	}
	cout << ans << '\n';
}