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 a[200010];
int n,sum;
map<int,int>mp;
map<int,int>s;
bool pan(int x)
{
	int t=1;
	while (t<=x) t*=2;
	if (mp[t-x]) {
		mp[t-x]--; s[t-x]++; return 1;
	} else return 0;
}
int main()
{
	scanf("%d",&n);
    for (int i=1;i<=n;i++) scanf("%d",&a[i]);
    sort(a+1,a+n+1);
    for (int i=1;i<=n;i++) mp[a[i]]++;
    for (int i=n;i>=1;i--) 
     {
     	if (!s[a[i]]) 
     	{
		 mp[a[i]]--; 
		 if (pan(a[i])) sum++;
	    } 
		 else s[a[i]]--;
     	
	 }
    cout << sum << endl; 
}