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<iostream>
#include<set>
#include<cmath>
#include<algorithm>
using namespace std;
int main(){
  int i,n,t;
  cin >> n;
  multiset<int, std::greater<int>>a;
  for(i=0;i<n;i++){
    int t;
    cin>>t;
    a.insert(t);
  }
  int ans=0;
  while(!a.empty()){
    int x=*a.begin();
    a.erase(a.begin());
    int y=pow(2,(int)log2(x)+1)-x;
    auto it=a.find(y);
    if(it!=a.end()){
      a.erase(it);
      ans+=1;
    }
  }
  cout << ans << endl;
}
