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;

int a[222222], b[222222];
int main() {
	int n;
	cin >> n;
	for (int i = 0; i < n; i++)
		scanf("%d", a + i);
	sort(a, a + n);
	int c = 0;
	while (n--) {
		if (b[n]) continue;
		for (int i = 1; i < 31; i++) {
			int x = (1 << i) - a[n];
			if (x <= 0) continue;
			int j = lower_bound(a, a + n, x) - a;
			if (j >= n || a[j] != x || b[j])
				continue;
			c++;
			int k = upper_bound(a, a + n, x) - a;
			while (b[--k]);
			b[k] = 1;
			break;
		}
	}
	cout << c << endl;
	return 0;
}
