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 a[200010];
map <int, int> mp;

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

int main(){
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++){
		scanf("%d", &a[i]);
		mp[a[i]]++;
    }
	sort(a, a + n), reverse(a, a + n);
	int res = 0;
	for (int i = 0; i < n; i++){
//		cout << a[i] << endl;
		if (mp[a[i]] == 0) continue;
		int tot = Get(a[i]);
		mp[a[i]]--;
		if (mp.count(tot - a[i]) && mp[tot - a[i]] != 0) mp[tot - a[i]]--, res++;
    }
	printf("%d\n", res);
	return 0;
}