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 <cstdio>
#include <set>
#include <algorithm>

int as[200005];

int invert(int X){
  int k=0;
  while((1<<k)<=X) k++;
  //printf("invert(%d)=%d\n",X,(1<<k)-X);
  return (1<<k)-X;
}

int main(){
  int N;
  scanf("%d",&N);
  for(int i=0;i<N;i++){
    scanf("%d",&as[i]);
  }
  std::sort(as,as+N);
  std::multiset<int> look;
  int match=0;
  for(int i=N-1;i>=0;i--){
    if(look.count(as[i])){
      look.erase(look.find(as[i]));
      match++;
    }else{
      look.insert(invert(as[i]));
    }
  }
  printf("%d\n",match);
  return 0;
}
