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, ans = 0;
	static int A[200000];
	map<int, int, greater<int> > mp;
	cin >> N;
	for (int i = 0; i < N; i++) cin >> A[i], mp[A[i]]++;
	sort(A, A + N, greater<int>());
	for (int i = 0; i < N; i++) {
		if (mp[A[i]] <= 0) continue;
		int B = pow(2, (int)log2(A[i]) + 1) - A[i];
		if (mp[B] <= 0) continue;
		if (B == A[i] && mp[A[i]] <= 1) continue;
		ans++;
		mp[A[i]]--;
		mp[B]--;
	}
	cout << ans;
}