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;
const int N=2e5+5;
int n,a[N];
unordered_map<int,int>vis;
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%d",&a[i]),vis[a[i]]++;
    sort(a+1,a+1+n);
    int ans=0;
    for(int i=n;i>=1;i--)
    {
        if(!vis[a[i]]) continue;
        vis[a[i]]--;
        for(int j=1<<30;j&&j>=a[i];j>>=1)
        {
            if(vis[j-a[i]])
            {
                vis[j-a[i]]--;
                ans++;
                break;
            }
        }
    }
    printf("%d\n",ans);
}
