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;
  map<int,int> A;
  for(int i=0;i<N;i++){
    int a;
    cin>>a;
    A[a]++;
  }
  int ans=0;
  while(A.size()){
    int j=(*prev(A.end())).first,k=1;
    for(;k<j;k*=2);
    if(k==j){
      ans+=A[j]/2;
      A.erase(j);
      continue;
    }
    if(A.count(k-j)){
      A[k-j]--;
      if(!A[k-j])A.erase(k-j);
      ans++;
    }
    A[j]--;
    if(!A[j])A.erase(j);
  }
  cout<<ans<<endl;
}