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 N;
multiset <int> S;

int get(int x) {
	int res = 1;
	while (res <= x)
		res *= 2;
	return res;
}

int main() {
	scanf("%d", &N);
	while (N--) {
		int x;
		scanf("%d", &x);
		S.insert(x);
	}
	
	int ans = 0;
	while (!S.empty()) {
		int x = *S.rbegin();
		S.erase(S.find(x));
		if (S.empty())
			break;
		int pot = get(x);
		auto it = S.find(pot - x);
		if (it != S.end()) {
			S.erase(it);
			ans++;
		}
	}
	
	printf("%d\n", ans);
	
	return 0;
}