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 main() {
	int n; scanf("%d", &n);
	multiset<int> ms;
	for (int i = 0; i < n; ++i) {
		int u; scanf("%d", &u);
		ms.insert(u);
	}
	int ans = 0;
	while (ms.size()) {
		int u = *ms.rbegin(); ms.erase(ms.find(u));
		int v = 1;
		while (v <= u) v <<= 1;
		if (ms.find(v - u) != ms.end()) {
			++ans; ms.erase(ms.find(v - u));
		}
	}
	printf("%d\n", ans);
}