description: Let's call a set of positive integers a_1, a_2, ..., a_k quadratic if the product of the factorials of its elements is a square of an integer, i. e. ∏_{i=1}^{k} a_i! = m^2, for some integer m.
  
  You are given a positive integer n.
  
  Your task is to find a quadratic subset of a set 1, 2, ..., n of maximum size. If there are multiple answers, print any of them.
  
  Input
  
  A single line contains a single integer n (1 ≤ n ≤ 10^6).
  
  Output
  
  In the first line, print a single integer — the size of the maximum subset. In the second line, print the subset itself in an arbitrary order.
  
  Examples
  
  Input
  
  
  1
  
  
  Output
  
  
  1
  1 
  
  
  Input
  
  
  4
  
  
  Output
  
  
  3
  1 3 4 
  
  
  Input
  
  
  7
  
  
  Output
  
  
  4
  1 4 5 6 
  
  
  Input
  
  
  9
  
  
  Output
  
  
  7
  1 2 4 5 6 7 9 
solution: def T(n):
      return int(n**0.5)**2 == n
  
  def solve(n):
      if n % 4 == 0: return [n//2]
      if n == 1: return []
      if n % 4 == 1: return [n//2, n]
      if n % 4 == 2:
          if T(n + 2): return [n//2 + 1]
          if T(n * (n//2 - 1)): return [n//2 - 2]
          return [n//2, 2]
      else:
          if T(n + 1): return [n//2 + 1, n]
          if T(2*(n//2)*(n//2 - 1)): return [n, n//2 - 2]
          if T((n//2-1) * n): return [n//2 - 2, n-2]
          return [2, n//2, n]
  
  if __name__ == '__main__':
      n = int(input())
      arr = solve(n)
      ans = [i for i in range(1, n+1) if i not in arr]
      print(len(ans))
      print(" ".join(str(i) for i in ans))
  