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<iostream>
#include<algorithm>
using namespace std;
int main() {
	static int N, A[200000], ans = 0;
	cin >> N;
	for (int i = 0;i < N;++ i) cin >> A[i];
	sort(A, A+N);
	for (int i = 1 << 30;i > 0;i >>= 1) {
		for (int j = 0, k = N - 1;j < k;) {
			if (A[j] < 0 || A[k] > 0 && A[j] + A[k] < i) ++ j;
			else if (A[k] < 0 || A[j] + A[k] > i) -- k;
			else {
				A[j] = A[k] = -1;
				++ ans;
			}
		}
	}
	cout << ans;
	return 0;
}