




def 		snake_case(    __magic_name__   )			->							list[list[int]]:





     '''simple docstring'''


     lowercase :       List[Any]       =			[]
     if len(__magic_name__   ) == 1:
          return [nums.copy()]
     for _ in range(len(__magic_name__   )   ):
          lowercase :       Optional[Any]       =			nums.pop(0   )
          lowercase :       Optional[int]       =			permute(__magic_name__   )
          for perm in permutations:
               perm.append(__magic_name__   )
          result.extend(__magic_name__   )
          nums.append(__magic_name__   )
     return result






def 		snake_case(    __magic_name__   )			->							List[Any]:





     '''simple docstring'''


     def backtrack(__magic_name__   ):
          if start == len(__magic_name__   ) - 1:
               output.append(nums[:]   )
          else:
               for i in range(__magic_name__			,		len(__magic_name__   )   ):
                    lowercase :       Tuple       =			nums[i], nums[start]
                    backtrack(start + 1   )
                    lowercase :       Optional[int]       =			nums[i], nums[start]  # backtrack

     lowercase :       Optional[int]       =			[]
     backtrack(0   )
     return output


if __name__ == "__main__":
 import doctest

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





import math






def  snake_case(    __magic_name__   )			->							bool:





     '''simple docstring'''


     lowercase :       Union[str, Any]       =			math.loga(math.sqrt(4 * positive_integer + 1   ) / 2 + 1 / 2   )

     return exponent == int(__magic_name__   )






def  snake_case(    __magic_name__ = 1 / 1_23_45   )			->							int:





     '''simple docstring'''


     lowercase :       Union[str, Any]       =			0
     lowercase :       str       =			0

     lowercase :       Optional[int]       =			3
     while True:
          lowercase :       Any       =			(integer**2 - 1) / 4
          # if candidate is an integer, then there is a partition for k
          if partition_candidate == int(__magic_name__   ):
               lowercase :       Any       =			int(__magic_name__   )
               total_partitions += 1
               if check_partition_perfect(__magic_name__   ):
                    perfect_partitions += 1
          if perfect_partitions > 0:
               if perfect_partitions / total_partitions < max_proportion:
                    return int(__magic_name__   )
          integer += 1


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