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;
	cin >> N;
	vector<int> A(N);
	for (auto& x : A) cin >> x;
	sort(A.rbegin(), A.rend());
	map<int,int> a;
	int r = 0;
	for (auto x : A) {
		if (a.count(x) && a[x] > 0) {
			-- a[x];
			++ r;
		} else {
			int k = 0;
			for (int i = 0; i <= 30; ++ i) if ((x>>i)&1) k = i;
			int y = (1<<(k+1)) - x;
			++ a[y];
		}
	}
	cout << r << endl;
}
