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 <set>
int n, ans;
std::multiset<int> st;

int main() {
	int i, a, x, y;
	scanf("%d", &n);
	for(i=0; i<n; i++) scanf("%d", &a), st.insert(a);
	while(!st.empty()) {
		x = *st.rbegin();
		st.erase(st.find(x));
		for(y=1; y<=x; y<<=1);
		std::multiset<int>::iterator it = st.find(y-x);
		if(it != st.end()) ans++, st.erase(it);
	}
	printf("%d", ans);
	return 0;
}