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 ll;

ll keta(ll t){
  ll k = 0; 
  while(t > 0){
    t >>= 1;
    k++;
  }
  return k;
}

int main(){
  ll N;  cin >> N;
  multiset<ll> a;
  for(ll i = 0; i < N; i++){
    ll tmp; cin >> tmp;
    a.emplace(tmp);
  }
  ll ans = 0;
  
  while(a.size() > 1){
    auto it = a.end();
    it--;
    a.erase(it);
    ll pr = (1 << keta(*it)) - *it;
    auto pit = a.find(pr);
    if(pit != a.end()){
      ans++;
      a.erase(pit);
    }
  }
  cout << ans;
}