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;

const int N = (int)2e5 + 7;

int a[N];
int n;
map < int, int > mp;

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i++) {
		scanf("%d", &a[i]);
		mp[a[i]]++;
	}
	int ans = 0;
	sort(a + 1, a + n + 1);
	for (int i = n; i >= 1; i--) {
		if (mp[a[i]] == 0) continue;
		int cur = 1;
		while (cur <= a[i]) cur <<= 1;
		if (mp[cur - a[i]] > (cur == a[i] + a[i])) {
			ans++;
			mp[a[i]]--;
			mp[cur - a[i]]--;
		}
	}
	cout << ans;
}
