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;

#define rep(i, n) for(int i = 0; i < (int)n; i++)

typedef long long ll;

int beki(int x)
{
	int s=0, tmp=1;
	while(tmp<=x)
	{
		s++;
		tmp*=2;
	}
	return tmp;
}

int main()
{
	int n;
	int a[200010];
	cin >> n;
	rep(i, n) cin >> a[i];
	sort(a, a+n);
	map<int, int> T;
	rep(i, n) T[a[i]]++;
	int ans=0;
	for(int i=n-1; i>0; i--)
	{
      	T[a[i]]--;
		int tmp=beki(a[i])-a[i];
		if(T[a[i]]>=0 && T[tmp]>0)
		{
			ans++;
			T[tmp]--;
		}
	}
	cout << ans << endl;
	return 0;
}