from itertools import permutations







def 						UpperCAmelCase							(		lowerCAmelCase_ = 5							)						->						int:
     if gon_side < 3 or gon_side > 5:
          raise ValueError('''gon_side must be in the range [3, 5]'''							)

     # Since it's 16, we know 10 is on the outer ring
     # Put the big numbers at the end so that they are never the first number
     a	:     Dict						      =    list(range(gon_side + 1    ,   0    ,   -1							)							)
     a	:     Optional[Any]						      =    list(range(gon_side + 2    ,   gon_side * 2 + 1							)							)

     for perm in permutations(small_numbers + big_numbers							):
          a	:     Optional[Any]						      =    generate_gon_ring(lowerCAmelCase_    ,   list(lowerCAmelCase_							)							)
          if is_magic_gon(lowerCAmelCase_							):
               return int(''''''.join(str(lowerCAmelCase_							) for n in numbers							)							)

     a	:     List[Any]						      =    f"""Magic {gon_side}-gon ring is impossible"""
     raise ValueError(lowerCAmelCase_							)







def 						UpperCAmelCase							(		lowerCAmelCase_    ,   lowerCAmelCase_							)						->						list[int]:
     a	:     Dict						      =    [0] * (gon_side * 3)
     a	:     Optional[int]						      =    perm[0:3]
     perm.append(perm[1]							)

     a	:     Dict						      =    1 if gon_side < 5 else 2

     for i in range(1    ,   len(lowerCAmelCase_							) // 3 + magic_number							):
          a	:     Any						      =    perm[2 * i + 1]
          a	:     List[Any]						      =    result[3 * i - 1]
          a	:     Union[str, Any]						      =    perm[2 * i + 2]

     return result







def 						UpperCAmelCase							(		lowerCAmelCase_							)						->						bool:
     if len(lowerCAmelCase_							) % 3 != 0:
          raise ValueError('''a gon ring should have a length that is a multiple of 3'''							)

     if min(numbers[::3]							) != numbers[0]:
          return False

     a	:     int						      =    sum(numbers[:3]							)

     return all(sum(numbers[i : i + 3]							) == total for i in range(3    ,   len(lowerCAmelCase_							)    ,   3							)							)


if __name__ == "__main__":
  print(solution())
UpperCAmelCase				 =   {
    0: """underwear""",
    1: """pants""",
    2: """belt""",
    3: """suit""",
    4: """shoe""",
    5: """socks""",
    6: """shirt""",
    7: """tie""",
    8: """watch""",
}

UpperCAmelCase				 =   [[1, 4], [2, 4], [3], [], [], [4], [2, 7], [3], []]

UpperCAmelCase				 =   [0 for x in range(len(graph))]
UpperCAmelCase				 =   []







def 						UpperCAmelCase							(		lowerCAmelCase_    ,   lowerCAmelCase_							)						->						List[Any]:
     a	:     Tuple						      =    1
     while stack:
          a	:     Optional[Any]						      =    stack.pop()
          print(lowerCAmelCase_    ,   clothes[current_clothing]							)
          order += 1







def 						UpperCAmelCase							(		lowerCAmelCase_    ,   lowerCAmelCase_    ,   lowerCAmelCase_							)						->						Any:
     a	:     Union[str, Any]						      =    1
     for v in graph[u]:
          if not visited[v]:
               depth_first_search(lowerCAmelCase_    ,   lowerCAmelCase_    ,   lowerCAmelCase_							)

     stack.append(lowerCAmelCase_							)







def 						UpperCAmelCase							(		lowerCAmelCase_    ,   lowerCAmelCase_							)						->						Optional[Any]:
     for v in range(len(lowerCAmelCase_							)							):
          if not visited[v]:
               depth_first_search(lowerCAmelCase_    ,   lowerCAmelCase_    ,   lowerCAmelCase_							)


if __name__ == "__main__":
  topological_sort(graph, visited)
  print(stack)
  print_stack(stack, clothes)