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 n,a[200001],ans;
map<int,int> mp;
int Get(int x)
{
	int res=1;
	while (res<=x) res*=2;
	return res;
}
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	cin>>n;
	for (int i=0;i<n;++i) cin>>a[i],++mp[a[i]];
	sort(a,a+n);
	reverse(a,a+n);
	for (int i=0;i<n;++i)
	{
		if (mp[a[i]]==0) continue;
		int tot=Get(a[i]);
		--mp[a[i]];
		if (mp.count(tot-a[i]) && mp[tot-a[i]]!=0) --mp[tot-a[i]],++ans;
    }
	cout<<ans;
	return 0;
}