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;

map <int, int> mp;

int main(){
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++){
		int x; scanf("%d", &x);
		mp[x]++;
	}
	int res = 0;
	while (!mp.empty()){
		map <int, int> :: iterator it = mp.end();
		it--;
		int x = it->first;
		mp[x]--;
		if (mp[x] == 0) mp.erase(x);
		int tot;
		for (tot = 1; tot <= x; tot <<= 1);
		if (mp.count(tot - x)){
			mp[tot - x]--, res++;
			if (mp[tot - x] == 0) mp.erase(tot - x);
		}
	}
	printf("%d\n", res);
	return 0;
}
