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;

//https://atcoder.jp/contests/agc029/tasks/agc029_b

int n, ans = 0;
multiset<int> s;

int main() {
	cin >> n;
	for (int i = 0; i < n; ++i) {
		int a;
		cin >> a;
		s.insert(a);
	}
	while (!s.empty()) {
		auto a = s.end();
		--a;
		s.erase(a);
		int b = 1;
		while (b <= *a)
			b <<= 1;
		auto c = s.find(b - *a);
		if (c != s.end()) {
			++ans;
			s.erase(c);
		}
	}
	cout << ans << endl;
}
