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(){
	ios::sync_with_stdio(false);
	cin.tie(0);  
	int n;
	cin >> n;
	vector<long long> a(n);
	map<long long, int> mp;
	for(int i = 0; i < n; i++) {
		cin >> a[i];
		mp[a[i]]++;
	}
	sort(a.rbegin(), a.rend());
	long long ans = 0;
	for(int i = 0; i < n; i++) {
		if(mp[a[i]] <= 0) {
			continue;
		}
		mp[a[i]]--;
		for(long long j = 1; j <= 2 * 1e9 + 1; j <<= 1) {
			if(mp.count(j - a[i])) {
				if(mp[j - a[i]] > 0) {
					mp[j - a[i]]--;
					ans++;
				}
			}
		}
	}
	cout << ans << endl;
	return 0;	
}
