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>
#define long long long
using namespace std;
const int N=1e6;
int main()
{
  ios_base::sync_with_stdio(0);cin.tie(0);

  int n;cin>>n;multiset<int>st;
  for(int i=1;i<=n;i++)
  {
    int x;cin>>x;st.insert(x);
  }
  int ans=0;
  while(st.size())
  {
    int x=*st.rbegin();
    st.erase(st.find(x));

    for(int i=30;i>=0;i--)
    {
      int z=(1<<i)-x;
      if(z<0)break;
      if(st.find(z)!=st.end())
      {
        ans++;st.erase(st.find(z));
        break;
      }
    }
  }
  cout<<ans<<endl;
  return 0;
}
