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;

int upper_b(int x){
  int cnt=1;
  while(x){
    x/=2;
    cnt*=2;
  }
  return cnt;
}

int main(){
  int N,a,ans=0;
  cin>>N;
  multiset<int> S;
  for(int i=0;i<N;i++){
    cin>>a;
    S.insert(a);
  }
  auto it=S.end();
  while(!S.empty()){
    it=S.end();
    it--;
    a=upper_b(*it);
    a-=*it;
    S.erase(it);
    
    it=S.find(a);
    if(it!=S.end()){
      S.erase(it);
      ans++;
    }
  }
  cout<<ans<<endl;
}