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 <iostream>
#include <algorithm>
#include <map>
using namespace std;
int arr[200005];
map<int,int> cnt;
int main()
{
	int n,ans=0;
	scanf("%d",&n);
	for (int i=0;i<n;i++)
	{
		scanf("%d",&arr[i]);
		cnt[arr[i]]++;
	}
	sort(arr,arr+n);
	for (int i=n-1;i>=0;i--)
	{
		if (!cnt[arr[i]])
		continue;
		cnt[arr[i]]--;
		int pw=1;
		while (pw<=arr[i])
		pw*=2;
		if (cnt[pw-arr[i]])
		{
			cnt[pw-arr[i]]--;
			ans++;
		}
	}
	printf("%d",ans);
}