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;
const int maxn = 2e5 + 10;
int n, ans;
int a[maxn];
priority_queue<int> Q;
int main()
{
	scanf("%d", &n); 
	for(int i = 1; i <= n; ++i) scanf("%d", &a[i]);
	sort(a + 1, a + n + 1, greater<int>());
	for(int i = 1; i <= n; ++i)
	{
		while(!Q.empty() && Q.top() > a[i]) Q.pop();
		if(!Q.empty() && Q.top() == a[i])
		{
			++ans;
			Q.pop();
			continue;
		}
		int k = 1 << (32 - __builtin_clz(a[i]));
		Q.push(k - a[i]);
	}
	printf("%d\n", ans);
	return 0;
}
		