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 mk make_pair
using namespace std;
typedef long long ll;
const int N = 3e5 + 5;
int n, m, a[N], ans;
int main() {
	cin >> n;
	for (int i = 1; i <= n; ++i) {
		scanf("%d", a + i);
	}
	sort(a + 1, a + 1 + n);
	for (int i = 30; i > 0; --i) {
		int p = n, tmp = 1 << i;
		for (int j = 1; j <= n; ++j) {
			if (a[j] == 0) continue;
			while (p > j && (a[p] == 0 || a[p] > tmp - a[j])) --p;
			if (p > j && a[p] + a[j] == tmp) {
				ans++;
				a[j] = a[p] = 0;
			}
		}
	}
	cout << ans;
}