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;
multiset <int> s;
int n,ans;
int main()
{
    scanf("%d",&n);
    while(n--)
    {
        int a;
        scanf("%d",&a);
        s.insert(a);
    }
    while(!s.empty())
    {
        int t = *(--s.end()),k;
        for(k=1;k<=t;k*=2);
        s.erase(--s.end());
        if(s.find(k-t)!=s.end())
        {
            ans++;
            s.erase(s.find(k-t));
        }
    }
    printf("%d",ans);
}
