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 <cstdio>
#include <map>
#include <algorithm>

std::map<int, int> mp; 
int a[201000];

int main()
{
	int n, ans = 0; scanf("%d", &n);
	for(int i = 1; i <= n; i++)
	{
		scanf("%d", &a[i]);
		mp[a[i]]++;
	}
	std::sort(a + 1, a + n + 1);
	for(int i = n; i >= 1; i--)
	{
		if(!mp[a[i]]) continue;
		mp[a[i]]--;
		int j = 1;
		for(j = 1; ; j <<= 1) if(j > a[i]) break;
		if(mp[j - a[i]]) ans++, mp[j - a[i]]--;
	}
	printf("%d\n", ans);
}