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<algorithm>
#include<set>
using namespace std;

multiset<int> nums;
int n;

int opposite(int x){
  int k = 1;
  while(k <= x)k *= 2;
  return k-x;
}
int a;
int main(){
  cin >> n;
  for(int i = 0;i < n;i++){
    cin >> a;
    nums.insert(-a);
  }
  int res = 0;
  while(nums.size() >= 2){
    int a = -*nums.begin();
    nums.erase(nums.begin());
    if(nums.find(-opposite(a)) == nums.end())continue;
    res++;
    nums.erase(nums.find(-opposite(a)));
  }
  cout << res << endl;
}