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;
#define int long long

signed main(){

  int n; cin >> n;
  multimap<int,int> mp;
  for(int i = 0; i < n; i++){
    int a; cin >> a;
    mp.insert({a,1});
  }

  int ans = 0;
  for(; !mp.empty();){
    auto p = mp.end();
    p--;
    int t = 1;
    while(p->first >= t) t *= 2;
    mp.erase(p);
    if(mp.find(t-p->first) != mp.end()){
      mp.erase(mp.find(t-p->first));
      ans++;
    }
  }
  cout << ans << endl;

  return 0;
}
