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 <cstdio>
#include <iostream>
#include <algorithm>
#include <map>
using namespace std;
map<int,int > f;
int n,a[444444];
int lb(int x)
{return x&(-x);}
int main()
{
    int as=0;
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%d",&a[i]),++f[a[i]];
    sort(a+1,a+n+1);
    for(int i=n;i;--i)
        if(f[a[i]])
        {
            --f[a[i]];
            int now=a[i];
            while(lb(now)!=now)now^=lb(now);
            now<<=1;
            if(f[now-a[i]])++as,--f[now-a[i]];
        }
    return printf("%d",as),0;
}