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;

const int N = 200100;

int a[N];
multiset <int> s;

int main() {
	int n;
	scanf("%d", &n);

	for (int i = 0; i < n; ++i) {
		scanf("%d", &a[i]);
		s.insert(a[i]);
	}

	sort(a, a+n);

	int ans = 0;
	for (int i = n-1; i >= 0; --i) {
		if(s.find(a[i]) != s.end()) {
			s.erase(s.find(a[i]));
			int at = a[i];
			int nxt = (1 << (32 - __builtin_clz(at))) - at;
			if(s.find(nxt) != s.end()) {
				s.erase(s.find(nxt));
				ans++;
			}
		}
	}
	printf("%d\n", ans);

}