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>
#define err(...) fprintf(stderr, __VA_ARGS__), fflush(stderr)

typedef long long ll;

using namespace std;

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n; cin >> n;

	multiset<int> S;
	for (int i = 0; i < n; i++) {
		int x; cin >> x;
		S.insert(x);
	}
	
	int ans = 0;
	while (S.size()) {
		int t = *S.rbegin();
		S.erase(--S.end());
		
		int p = 1;
		while (p <= t) p *= 2;
		
		if (S.find(p - t) != S.end()) {
			ans++;
			S.erase(S.find(p - t));
		}
	}
	cout << ans << "\n";
	return 0;
}
