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>

using namespace std;

typedef long long int ll;

int main(){
  ios_base::sync_with_stdio(false);
  cin.tie(0);cout.tie(0);

  int n;
  cin >> n;
  vector < int > a(n);
  for(int i = 0; i < n; i++) cin >> a[i];
  multiset < int > s(a.begin(), a.end());

  int ans = 0;
  while(!s.empty()){
    auto it = prev(s.end());
    int x = *it;
    int y = (1 << (32 - __builtin_clz(x))) - x;
    s.erase(it);
    it = s.find(y);
    if(it != s.end()){
      ans++;
      s.erase(it);
    }
  }

  cout << ans << '\n';
}
