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;
long long N, A[200009], cnt;
multiset<long long> S;
int main() {
	cin >> N;
	for (int i = 0; i < N; i++) cin >> A[i];
	sort(A, A + N);
	for (int i = N - 1; i >= 0; i--) {
		bool flag = false;
		for (int j = 0; j < 32; j++) {
			long long ret = (1LL << j) - A[i];
			if (A[i] > ret) continue;
			auto itr = S.lower_bound(ret);
			if (itr != S.end() && *itr == ret) {
				S.erase(itr);
				cnt++;
				flag = true;
				break;
			}
		}
		if (flag == false) {
			S.insert(A[i]);
		}
	}
	cout << cnt << endl;
}