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;
unordered_map<long long , int> um;

int main(){
  int N;cin >> N;
  vector<long long> V(N);
  for(auto&&e:V){
    cin >> e;
    um[e]++;
  }
  sort(V.begin(), V.end(), greater<long long>());
  int ans = 0;
  for(int i = 0; i < N; ++i){
    if(um[V[i]] < 1)continue;
    um[V[i]]--;
    long long nx = 1;
    while(nx <= V[i])nx<<=1;
    nx -= V[i];
    if(um.count(nx)==0)continue;
    int c = um[nx];
    if(c < 1)continue;
    um[nx]--;
    ans++;
  }
  cout << ans << endl;
  return 0;
}
