


from math import ceil


def 				lowerCamelCase__	(      a	:   Optional[int]	,  a	:   str				)    ->	List[str]:





   """simple docstring"""
   a__ :Union[str, Any]						  =    list(range(0	,  a				)				)

   a__ :int						  =    [item for sublist in list(device_map.values()				) for item in sublist]

   # Duplicate check
   a__ :Dict						  =    []
   for i in device_map_blocks:
      if device_map_blocks.count(a				) > 1 and i not in duplicate_blocks:
         duplicate_blocks.append(a				)
    # Missing blocks
   a__ :Optional[int]						  =    [i for i in blocks if i not in device_map_blocks]
   a__ :List[Any]						  =    [i for i in device_map_blocks if i not in blocks]

   if len(a				) != 0:
      raise ValueError(
          "Duplicate attention blocks specified in device_map. Attention blocks must be specified to one device."
          " These attention blocks were specified more than once: " + str(a				)				)
   if len(a				) != 0:
      raise ValueError(
          "There are attention blocks for this model that are not specified in the device_map. Add these attention "
          "blocks to a device on the device_map: " + str(a				)				)
   if len(a				) != 0:
      raise ValueError(
          "The device_map contains more attention blocks than this model has. Remove these from the device_map:"
          + str(a				)				)







def 				lowerCamelCase__	(      a	:   List[Any]	,  a	:   Dict				)    ->	str:





   """simple docstring"""
   a__ :Optional[Any]						  =    list(range(a				)				)
   a__ :List[str]						  =    int(ceil(n_layers / len(a				)				)				)
   a__ :Union[str, Any]						  =    [layers[i : i + n_blocks] for i in range(0	,  a	,  a				)]

   return dict(zip(a	,  a				)				)






def 				lowerCamelCase__	(      a	:   list[list]				)    ->	list[list]:





			"""simple docstring"""
			a__ :Any						  =    current_set.copy()
			for row_index, row in enumerate(a				):
						a__ :List[str]						  =    row[0]
						for column_index, column in enumerate(a				):
									if magnitude == 0:
												a__ :Tuple						  =    column
												continue
									a__ :Tuple						  =    column / magnitude
    # Subtract to cancel term
			a__ :Any						  =    current_set[0]
			a__ :Dict						  =    [first_row]
			a__ :Dict						  =    current_set[1::]
			for row in current_set:
						a__ :int						  =    []
						# If first term is 0, it is already in form we want, so we preserve it
						if row[0] == 0:
									final_set.append(a				)
									continue
						for column_index in range(len(a				)				):
									temp_row.append(first_row[column_index] - row[column_index]				)
						final_set.append(a				)
			# Create next recursion iteration set
			if len(final_set[0]				) != 3:
						a__ :List[str]						  =    final_set[0]
						a__ :Optional[Any]						  =    []
						a__ :List[Any]						  =    []
						for row in final_set[1::]:
									current_first_column.append(row[0]				)
									next_iteration.append(row[1::]				)
						a__ :Dict						  =    simplify(a				)
						for i in range(len(a				)				):
									resultant[i].insert(0	,  current_first_column[i]				)
						resultant.insert(0	,  a				)
						a__ :Optional[int]						  =    resultant
			return final_set


def 				lowerCamelCase__	(      a	:   list[list]				)    ->	list:





			"""simple docstring"""
			if len(a				) == 0:
						raise IndexError("solve_simultaneous() requires n lists of length n+1"				)
			a__ :Any						  =    len(a				) + 1
			if any(len(a				) != _length for item in equations				):
						raise IndexError("solve_simultaneous() requires n lists of length n+1"				)
			for row in equations:
						if any(not isinstance(a	,  (int, float)				) for column in row				):
									raise ValueError("solve_simultaneous() requires lists of integers"				)
			if len(a				) == 1:
						return [equations[0][-1] / equations[0][0]]
			a__ :Union[str, Any]						  =    equations.copy()
			if any(0 in row for row in data_set				):
						a__ :int						  =    data_set.copy()
						a__ :Dict						  =    []
						for row_index, row in enumerate(a				):
									if 0 not in row:
												a__ :Union[str, Any]						  =    data_set.pop(a				)
												break
						if not full_row:
									raise ValueError("solve_simultaneous() requires at least 1 full equation"				)
						data_set.insert(0	,  a				)
			a__ :Optional[int]						  =    data_set.copy()
			a__ :Any						  =    simplify(a				)
			a__ :str						  =    simplified[::-1]
			a__ :list						  =    []
			for row in simplified:
						a__ :Optional[int]						  =    row[-1]
						if not solutions:
									if row[-2] == 0:
												solutions.append(0				)
												continue
									solutions.append(current_solution / row[-2]				)
									continue
						a__ :Dict						  =    row.copy()[: len(a				) - 1 :]
						while temp_row[0] == 0:
									temp_row.pop(0				)
						if len(a				) == 0:
									solutions.append(0				)
									continue
						a__ :List[Any]						  =    temp_row[1::]
						a__ :Union[str, Any]						  =    temp_row[::-1]
						for column_index, column in enumerate(a				):
									current_solution -= column * solutions[column_index]
						solutions.append(a				)
			a__ :List[str]						  =    []
			for item in solutions:
						final.append(float(round(a	,  5				)				)				)
			return final[::-1]


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		snake_case__			 =						[
		    [2, 1, 1, 1, 1, 4],
		    [1, 2, 1, 1, 1, 5],
		    [1, 1, 2, 1, 1, 6],
		    [1, 1, 1, 2, 1, 7],
		    [1, 1, 1, 1, 2, 8],
		]
		print(solve_simultaneous(eq))
		print(solve_simultaneous([[4, 2]]))


