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;

signed main(){
	int n,a[200010];
	cin >> n;
	map<int,int> counts;
	for(int i = 0;i < n;i++){
		cin >> a[i];
		counts[a[i]]++;
	}
	sort(a,a + n,greater<int>());
	int ans = 0;
	for(int i = 0;i < n;i++){
		int v = (1 << (32 - __builtin_clz(a[i]))) - a[i];
		if((a[i] == v && counts[v] >= 2) || (a[i] != v && counts[v] && counts[a[i]])){
			counts[v]--; counts[a[i]]--;
			ans++;
		}
	}
	cout << ans << endl;
}