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 maxn 200010
using namespace std;
int val[maxn];
multiset<int> S;
int main()
{
	int n;
	scanf("%d", &n);
	for (int i = 1; i <= n; i++)
	{
		scanf("%d", &val[i]);
		S.insert(val[i]);
	}
	int res = 0;
	while (!S.empty())
	{
		multiset<int>::iterator it = S.end();
		it--;
		int tmp = *it, need = 1;
		S.erase(S.find(tmp));
		while (need <= tmp) need *= 2;
		if (S.find(need - tmp) != S.end())
		{
			res++;
			S.erase(S.find(need - tmp));
		}
	}
	printf("%d\n", res);
	return 0;
}