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>
#define int long long
using namespace std;

signed main(){
  int N;cin>>N;
  int a;
  map<int,int> m;
  for(int i=0;i<N;i++){
    cin>>a;
    m[a]++;
  }
  int k=1;
  set<int> s;
  for(int i=0;i<35;i++){
    s.emplace(k);
    k*=2;
  }
  int ans=0;
  for(auto p=m.rbegin();p!=m.rend();p++){
    while((p->second)>0){
      (p->second)--;
      if(m[*s.upper_bound(p->first)-(p->first)]>0){
        ans++;
        m[*s.upper_bound(p->first)-(p->first)]--;
      }
    }
  }
  cout<<ans<<endl;
}
