

"""simple docstring"""




def   lowerCAmelCase						(					__UpperCamelCase = 50      ):
 '''simple docstring'''





 UpperCAmelCase__					:  str					   =					[[0] * 3 for _ in range(length + 1      )]

 for row_length in range(length + 1      ):
  for tile_length in range(2							,    5      ):
   for tile_start in range(row_length - tile_length + 1      ):
    different_colour_ways_number[row_length][tile_length - 2] += (
        different_colour_ways_number[row_length - tile_start - tile_length][
            tile_length - 2
        ]
        + 1
    )

 return sum(different_colour_ways_number[length]      )


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








"""simple docstring"""




def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 UpperCAmelCase__					:  str					   =					[]
 if len(__UpperCamelCase      ) == 1:
  return [nums.copy()]
 for _ in range(len(__UpperCamelCase      )      ):
  UpperCAmelCase__					:  Tuple					   =					nums.pop(0      )
  UpperCAmelCase__					:  List[str]					   =					permute(__UpperCamelCase      )
  for perm in permutations:
   perm.append(__UpperCamelCase      )
  result.extend(__UpperCamelCase      )
  nums.append(__UpperCamelCase      )
 return result
def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 def backtrack(__UpperCamelCase      ):
  if start == len(__UpperCamelCase      ) - 1:
   output.append(nums[:]      )
  else:
   for i in range(__UpperCamelCase							,    len(__UpperCamelCase      )      ):
    UpperCAmelCase__   ,      UpperCAmelCase__					:  Union[str, Any]					   =					nums[i], nums[start]
    backtrack(start + 1      )
    UpperCAmelCase__   ,      UpperCAmelCase__					:  Union[str, Any]					   =					nums[i], nums[start]  # backtrack

 UpperCAmelCase__					:  List[str]					   =					[]
 backtrack(0      )
 return output


if __name__ == "__main__":
      import doctest

      # use res to print the data in permute2 function
      __UpperCAmelCase =				permutea([1, 2, 3])
      print(res)
      doctest.testmod()





