#include <iostream>
#include <set>
using namespace std;

int main()
{
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  multiset<int> st;
  for(int i = 0; i < n; ++i)
  {
    int a;
    cin >> a;
    st.insert(a);
  }

  int ans = 0;
  while (!st.empty())
  {
    int last = *(--st.end());
    st.erase(--st.end());
    int two = 1;
    while (two <= last)
      two <<= 1;
    auto itr = st.find(two - last);
    if (itr == st.end())
      continue;
    ++ans;
    st.erase(itr);
  }
  cout << ans;
  return 0;
}

### Prompt

In cpp, your task is to solve the following problem:

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

### Response

```cpp
#include <iostream>
#include <set>
using namespace std;

int main()
{
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  multiset<int> st;
  for(int i = 0; i < n; ++i)
  {
    int a;
    cin >> a;
    st.insert(a);
  }

  int ans = 0;
  while (!st.empty())
  {
    int last = *(--st.end());
    st.erase(--st.end());
    int two = 1;
    while (two <= last)
      two <<= 1;
    auto itr = st.find(two - last);
    if (itr == st.end())
      continue;
    ++ans;
    st.erase(itr);
  }
  cout << ans;
  return 0;
}

```