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 main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int n;
    cin>>n;
    for(int i=0;i<n;i++){
        int x;
        cin>>x;
        S.insert(x);
    }
    int ans=0;
    while(!S.empty())
    {
        int x=*S.rbegin();
        int y=1;
        S.erase(S.find(x));
        while(y<=x)
            y*=2;
        auto it=S.find(y-x);
        if(it!=S.end()){
            ans++;
            S.erase(it);
        }
    }
    cout<<ans;

}
