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(void){
  multiset<long,greater<long>>ball;
  size_t n;cin>>n;
  for(int i=0;i<n;i++){
    int x;cin>>x;
    ball.insert(x);
  }
  int ans=0;
  while(!ball.empty()){
    int x=*ball.begin();ball.erase(ball.begin());
    int y=pow(2,(int)log2(x)+1)-x;
    auto it=ball.find(y);
    if(it!=ball.end()){
      ball.erase(it);
      ans+=1;
    }
  }
  cout<<ans<<endl;
}