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;

void del(map<ll,ll> &mp, ll val){
  mp[val]--;
  if(mp[val] == 0){ mp.erase(val);}
}

int main(){
  ll N; cin >> N; map<ll,ll> mp;
  ll ans = 0;
  vector<ll> A(N); 
  for(ll i = 0; i < N; i++){ 
    cin >> A[i]; mp[-A[i]]++;}
  
  for(ll i = 0; i < N && !mp.empty(); i++){
    ll a = -mp.begin()->first;
    del(mp,-a);
    ll p = 1;
    while( p <= a){ p *= 2;}
    ll rem = a-p;
    if(mp.count(rem)){
      ans++;
      del(mp,rem);}
  }
  
  cout << ans << endl;
  return 0;}
      