





from __future__ import annotations

import math




def     a__ (					lowercase__  ):






   '''simple docstring'''






   if 1 < number < 4:
      # 2 and 3 are primes
      return True
   elif number < 2 or number % 2 == 0 or number % 3 == 0:
      # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
      return False

   # All primes number are in format of 6k +/- 1
   for i in range(5  ,    int(math.sqrt(lowercase__  ) + 1  )  ,    6  ):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True


__lowercase  :   Union[str, Any]						      =[num for num in range(3, 10_0001, 2) if not is_prime(num)]




def     a__ (					lowercase__  ):






   '''simple docstring'''






   if not isinstance(lowercase__  ,    lowercase__  ):
      raise ValueError("n must be an integer"  )
   if n <= 0:
      raise ValueError("n must be >= 0"  )

   UpperCAmelCase_											=[]
   for num in range(len(lowercase__  )  ):
      UpperCAmelCase_											=0
      while 2 * i * i <= odd_composites[num]:
         UpperCAmelCase_											=odd_composites[num] - 2 * i * i
         if is_prime(lowercase__  ):
            break
         i += 1
      else:
         list_nums.append(odd_composites[num]  )
         if len(lowercase__  ) == n:
            return list_nums

   return []




def     a__ (					):






   '''simple docstring'''






   return compute_nums(1  )[0]


if __name__ == "__main__":
     print(f"""{solution() = }""")











from __future__ import annotations




def     a__ (					lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_						,       UpperCAmelCase_											=set(lowercase__  ), [start]

   while stack:
      UpperCAmelCase_											=stack.pop()
      explored.add(lowercase__  )
      # Differences from BFS:
      # 1) pop last element instead of first one
      # 2) add adjacent elements to stack without exploring them
      for adj in reversed(graph[v]  ):
         if adj not in explored:
            stack.append(lowercase__  )
   return explored


__lowercase  :   Dict						      ={
    """A""": ["""B""", """C""", """D"""],
    """B""": ["""A""", """D""", """E"""],
    """C""": ["""A""", """F"""],
    """D""": ["""B""", """D"""],
    """E""": ["""B""", """F"""],
    """F""": ["""C""", """E""", """G"""],
    """G""": ["""F"""],
}

if __name__ == "__main__":
     import doctest

     doctest.testmod()
     print(depth_first_search(G, """A"""))




