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 n, ans, a[200010];
map<int, int> am;
int main()
{
	scanf("%d", &n);
	for (int i = 0; i < n; i++)
	{
		scanf("%d", &a[i]);
		am[a[i]]++;
	}
	sort(a, a+n);
	reverse(a, a+n);
	for (int i = 0; i < n; i++)
	{
		if (!am[a[i]]) continue;
		am[a[i]]--;
		for (int b = 0; b <= 30; b++)
		{
			int p = (1 << b);
			if (p < a[i]) continue;
			if (am[p-a[i]])
			{
				am[p-a[i]]--;
				ans++;
			}
		}
	}
	printf("%d\n", ans);
}