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 <cstdio>
#include <iostream>
#include <algorithm> 
#include <cstring>
#include <map>
using namespace std;
const int N = 2e5 + 10;
map<int,int> h;
int n,a[N],ans;
int main() { 
	cin>>n;
	for (int i = 1; i <= n; i++) scanf("%d",&a[i]),h[a[i]]++;
	for (int t = 1 << 30; t>1; t>>=1) {
		for (int i = 1; i <= n; i++) {
			int ot = t - a[i];
			if (ot == a[i]) {
				if (h[a[i]] >= 2) {
					h[a[i]]-=2; ans++;
				}
				continue;
			}
			if (ot > 0 && h[ot] > 0 && h[a[i]] > 0) {
				h[ot]--;
				h[a[i]]--;
				ans++;
			}
		}
	}
	cout<<ans<<endl;
}