

'''simple docstring'''




import argparse

import torch

from diffusers import UNetaDConditionModel


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   int       ,   SCREAMING_SNAKE_CASE      :   List[Any]       ,   SCREAMING_SNAKE_CASE      :   str       ,   SCREAMING_SNAKE_CASE      :   Optional[Any]=None       ,   SCREAMING_SNAKE_CASE      :   Optional[int]=None       ,   SCREAMING_SNAKE_CASE      :   List[Any]=None						):
  assert isinstance(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						), "Paths should be a list of dicts containing 'old' and 'new' keys."

  # Splits the attention layers into three variables.
  if attention_paths_to_split is not None:
    for path, path_map in attention_paths_to_split.items():
      UpperCAmelCase													=	old_checkpoint[path]
      UpperCAmelCase													=	old_tensor.shape[0] // 3

      UpperCAmelCase													=	(-1, channels) if len(old_tensor.shape						) == 3 else (-1)

      UpperCAmelCase													=	old_tensor.shape[0] // config['num_head_channels'] // 3

      UpperCAmelCase													=	old_tensor.reshape((num_heads, 3 * channels // num_heads) + old_tensor.shape[1:]						)
      UpperCAmelCase							,      UpperCAmelCase							,      UpperCAmelCase													=	old_tensor.split(channels // num_heads       ,   dim=1						)

      UpperCAmelCase													=	query.reshape(SCREAMING_SNAKE_CASE						)
      UpperCAmelCase													=	key.reshape(SCREAMING_SNAKE_CASE						)
      UpperCAmelCase													=	value.reshape(SCREAMING_SNAKE_CASE						)

  for path in paths:
    UpperCAmelCase													=	path['new']

    # These have already been assigned
    if attention_paths_to_split is not None and new_path in attention_paths_to_split:
      continue

    if additional_replacements is not None:
      for replacement in additional_replacements:
        UpperCAmelCase													=	new_path.replace(replacement['old']       ,   replacement['new']						)

        # proj_attn.weight has to be converted from conv 1D to linear
    UpperCAmelCase													=	old_checkpoint[path['old']]
    UpperCAmelCase													=	['proj_attn.weight']
    UpperCAmelCase													=	['proj_out.weight', 'proj_in.weight']
    if any(k in new_path for k in names						):
      UpperCAmelCase													=	weight[:, :, 0]
    elif any(k in new_path for k in names_a						) and len(weight.shape						) > 2 and ".attentions." not in new_path:
      UpperCAmelCase													=	weight[:, :, 0]
    else:
      UpperCAmelCase													=	weight


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   Union[str, Any]       ,   SCREAMING_SNAKE_CASE      :   Tuple=0						):
  UpperCAmelCase													=	[]
  for old_item in old_list:
    UpperCAmelCase													=	old_item

    #         new_item = new_item.replace('norm.weight', 'group_norm.weight')
    #         new_item = new_item.replace('norm.bias', 'group_norm.bias')

    #         new_item = new_item.replace('proj_out.weight', 'proj_attn.weight')
    #         new_item = new_item.replace('proj_out.bias', 'proj_attn.bias')

    #         new_item = shave_segments(new_item, n_shave_prefix_segments=n_shave_prefix_segments)

    mapping.append({'old': old_item, 'new': new_item}						)

  return mapping


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   str       ,   SCREAMING_SNAKE_CASE      :   Union[str, Any]=1						):
  if n_shave_prefix_segments >= 0:
    return ".".join(path.split('.'						)[n_shave_prefix_segments:]						)
  else:
    return ".".join(path.split('.'						)[:n_shave_prefix_segments]						)


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   int       ,   SCREAMING_SNAKE_CASE      :   str=0						):
  UpperCAmelCase													=	[]
  for old_item in old_list:
    mapping.append({'old': old_item, 'new': old_item}						)

  return mapping


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   Dict       ,   SCREAMING_SNAKE_CASE      :   Optional[Any]=0						):
  UpperCAmelCase													=	[]
  for old_item in old_list:
    UpperCAmelCase													=	old_item.replace('in_layers.0'       ,   'norm1'						)
    UpperCAmelCase													=	new_item.replace('in_layers.2'       ,   'conv1'						)

    UpperCAmelCase													=	new_item.replace('out_layers.0'       ,   'norm2'						)
    UpperCAmelCase													=	new_item.replace('out_layers.3'       ,   'conv2'						)

    UpperCAmelCase													=	new_item.replace('emb_layers.1'       ,   'time_emb_proj'						)
    UpperCAmelCase													=	new_item.replace('skip_connection'       ,   'conv_shortcut'						)

    UpperCAmelCase													=	shave_segments(SCREAMING_SNAKE_CASE       ,   n_shave_prefix_segments=SCREAMING_SNAKE_CASE						)

    if "temopral_conv" not in old_item:
      mapping.append({'old': old_item, 'new': new_item}						)

  return mapping


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   Optional[Any]       ,   SCREAMING_SNAKE_CASE      :   int       ,   SCREAMING_SNAKE_CASE      :   Tuple=None       ,   SCREAMING_SNAKE_CASE      :   str=False						):
  UpperCAmelCase													=	{}
  UpperCAmelCase													=	list(checkpoint.keys()						)

  UpperCAmelCase													=	'model.diffusion_model.'

  # at least a 100 parameters have to start with `model_ema` in order for the checkpoint to be EMA
  if sum(k.startswith('model_ema'						) for k in keys						) > 100 and extract_ema:
    print(f'''Checkpoint {path} has both EMA and non-EMA weights.'''						)
    print(
        'In this conversion only the EMA weights are extracted. If you want to instead extract the non-EMA'
        ' weights (useful to continue fine-tuning), please make sure to remove the `--extract_ema` flag.'						)
    for key in keys:
      if key.startswith('model.diffusion_model'						):
        UpperCAmelCase													=	'model_ema.' + ''.join(key.split('.'						)[1:]						)
        UpperCAmelCase													=	checkpoint.pop(SCREAMING_SNAKE_CASE						)
  else:
    if sum(k.startswith('model_ema'						) for k in keys						) > 100:
      print(
          'In this conversion only the non-EMA weights are extracted. If you want to instead extract the EMA'
          ' weights (usually better for inference), please make sure to add the `--extract_ema` flag.'						)

    for key in keys:
      UpperCAmelCase													=	checkpoint.pop(SCREAMING_SNAKE_CASE						)

  UpperCAmelCase													=	{}

  UpperCAmelCase													=	unet_state_dict['time_embed.0.weight']
  UpperCAmelCase													=	unet_state_dict['time_embed.0.bias']
  UpperCAmelCase													=	unet_state_dict['time_embed.2.weight']
  UpperCAmelCase													=	unet_state_dict['time_embed.2.bias']

  if config["class_embed_type"] is None:
    # No parameters to port
    ...
  elif config["class_embed_type"] == "timestep" or config["class_embed_type"] == "projection":
    UpperCAmelCase													=	unet_state_dict['label_emb.0.0.weight']
    UpperCAmelCase													=	unet_state_dict['label_emb.0.0.bias']
    UpperCAmelCase													=	unet_state_dict['label_emb.0.2.weight']
    UpperCAmelCase													=	unet_state_dict['label_emb.0.2.bias']
  else:
    raise NotImplementedError(f'''Not implemented `class_embed_type`: {config['class_embed_type']}'''						)

  UpperCAmelCase													=	unet_state_dict['input_blocks.0.0.weight']
  UpperCAmelCase													=	unet_state_dict['input_blocks.0.0.bias']

  UpperCAmelCase													=	[v for v in unet_state_dict if v.startswith('input_blocks.0.1'						)]
  UpperCAmelCase													=	renew_attention_paths(SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	{'old': 'input_blocks.0.1', 'new': 'transformer_in'}
  assign_to_checkpoint(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]       ,   config=SCREAMING_SNAKE_CASE						)

  UpperCAmelCase													=	unet_state_dict['out.0.weight']
  UpperCAmelCase													=	unet_state_dict['out.0.bias']
  UpperCAmelCase													=	unet_state_dict['out.2.weight']
  UpperCAmelCase													=	unet_state_dict['out.2.bias']

  # Retrieves the keys for the input blocks only
  UpperCAmelCase													=	len({'.'.join(layer.split('.'						)[:2]						) for layer in unet_state_dict if 'input_blocks' in layer}						)
  UpperCAmelCase													=	{
      layer_id: [key for key in unet_state_dict if f'''input_blocks.{layer_id}''' in key]
      for layer_id in range(SCREAMING_SNAKE_CASE						)
  }

  # Retrieves the keys for the middle blocks only
  UpperCAmelCase													=	len({'.'.join(layer.split('.'						)[:2]						) for layer in unet_state_dict if 'middle_block' in layer}						)
  UpperCAmelCase													=	{
      layer_id: [key for key in unet_state_dict if f'''middle_block.{layer_id}''' in key]
      for layer_id in range(SCREAMING_SNAKE_CASE						)
  }

  # Retrieves the keys for the output blocks only
  UpperCAmelCase													=	len({'.'.join(layer.split('.'						)[:2]						) for layer in unet_state_dict if 'output_blocks' in layer}						)
  UpperCAmelCase													=	{
      layer_id: [key for key in unet_state_dict if f'''output_blocks.{layer_id}''' in key]
      for layer_id in range(SCREAMING_SNAKE_CASE						)
  }

  for i in range(1       ,   SCREAMING_SNAKE_CASE						):
    UpperCAmelCase													=	(i - 1) // (config['layers_per_block'] + 1)
    UpperCAmelCase													=	(i - 1) % (config['layers_per_block'] + 1)

    UpperCAmelCase													=	[
        key for key in input_blocks[i] if f'''input_blocks.{i}.0''' in key and f'''input_blocks.{i}.0.op''' not in key
    ]
    UpperCAmelCase													=	[key for key in input_blocks[i] if f'''input_blocks.{i}.1''' in key]
    UpperCAmelCase													=	[key for key in input_blocks[i] if f'''input_blocks.{i}.2''' in key]

    if f'''input_blocks.{i}.op.weight''' in unet_state_dict:
      UpperCAmelCase													=	unet_state_dict.pop(
          f'''input_blocks.{i}.op.weight'''						)
      UpperCAmelCase													=	unet_state_dict.pop(
          f'''input_blocks.{i}.op.bias'''						)

    UpperCAmelCase													=	renew_resnet_paths(SCREAMING_SNAKE_CASE						)
    UpperCAmelCase													=	{'old': f'''input_blocks.{i}.0''', 'new': f'''down_blocks.{block_id}.resnets.{layer_in_block_id}'''}
    assign_to_checkpoint(
        SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]       ,   config=SCREAMING_SNAKE_CASE						)

    UpperCAmelCase													=	[key for key in resnets if 'temopral_conv' in key]
    UpperCAmelCase													=	renew_temp_conv_paths(SCREAMING_SNAKE_CASE						)
    UpperCAmelCase													=	{
        'old': f'''input_blocks.{i}.0.temopral_conv''',
        'new': f'''down_blocks.{block_id}.temp_convs.{layer_in_block_id}''',
    }
    assign_to_checkpoint(
        SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]       ,   config=SCREAMING_SNAKE_CASE						)

    if len(SCREAMING_SNAKE_CASE						):
      UpperCAmelCase													=	renew_attention_paths(SCREAMING_SNAKE_CASE						)
      UpperCAmelCase													=	{'old': f'''input_blocks.{i}.1''', 'new': f'''down_blocks.{block_id}.attentions.{layer_in_block_id}'''}
      assign_to_checkpoint(
          SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]       ,   config=SCREAMING_SNAKE_CASE						)

    if len(SCREAMING_SNAKE_CASE						):
      UpperCAmelCase													=	renew_attention_paths(SCREAMING_SNAKE_CASE						)
      UpperCAmelCase													=	{
          'old': f'''input_blocks.{i}.2''',
          'new': f'''down_blocks.{block_id}.temp_attentions.{layer_in_block_id}''',
      }
      assign_to_checkpoint(
          SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]       ,   config=SCREAMING_SNAKE_CASE						)

  UpperCAmelCase													=	middle_blocks[0]
  UpperCAmelCase													=	[key for key in resnet_a if 'temopral_conv' in key]
  UpperCAmelCase													=	middle_blocks[1]
  UpperCAmelCase													=	middle_blocks[2]
  UpperCAmelCase													=	middle_blocks[3]
  UpperCAmelCase													=	[key for key in resnet_a if 'temopral_conv' in key]

  UpperCAmelCase													=	renew_resnet_paths(SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	{'old': 'middle_block.0', 'new': 'mid_block.resnets.0'}
  assign_to_checkpoint(
      SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   config=SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]						)

  UpperCAmelCase													=	renew_temp_conv_paths(SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	{'old': 'middle_block.0.temopral_conv', 'new': 'mid_block.temp_convs.0'}
  assign_to_checkpoint(
      SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   config=SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]						)

  UpperCAmelCase													=	renew_resnet_paths(SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	{'old': 'middle_block.3', 'new': 'mid_block.resnets.1'}
  assign_to_checkpoint(
      SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   config=SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]						)

  UpperCAmelCase													=	renew_temp_conv_paths(SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	{'old': 'middle_block.3.temopral_conv', 'new': 'mid_block.temp_convs.1'}
  assign_to_checkpoint(
      SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   config=SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]						)

  UpperCAmelCase													=	renew_attention_paths(SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	{'old': 'middle_block.1', 'new': 'mid_block.attentions.0'}
  assign_to_checkpoint(
      SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]       ,   config=SCREAMING_SNAKE_CASE						)

  UpperCAmelCase													=	renew_attention_paths(SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	{'old': 'middle_block.2', 'new': 'mid_block.temp_attentions.0'}
  assign_to_checkpoint(
      SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]       ,   config=SCREAMING_SNAKE_CASE						)

  for i in range(SCREAMING_SNAKE_CASE						):
    UpperCAmelCase													=	i // (config['layers_per_block'] + 1)
    UpperCAmelCase													=	i % (config['layers_per_block'] + 1)
    UpperCAmelCase													=	[shave_segments(SCREAMING_SNAKE_CASE       ,   2						) for name in output_blocks[i]]
    UpperCAmelCase													=	{}

    for layer in output_block_layers:
      UpperCAmelCase							,      UpperCAmelCase													=	layer.split('.'						)[0], shave_segments(SCREAMING_SNAKE_CASE       ,   1						)
      if layer_id in output_block_list:
        output_block_list[layer_id].append(SCREAMING_SNAKE_CASE						)
      else:
        UpperCAmelCase													=	[layer_name]

    if len(SCREAMING_SNAKE_CASE						) > 1:
      UpperCAmelCase													=	[key for key in output_blocks[i] if f'''output_blocks.{i}.0''' in key]
      UpperCAmelCase													=	[key for key in output_blocks[i] if f'''output_blocks.{i}.1''' in key]
      UpperCAmelCase													=	[key for key in output_blocks[i] if f'''output_blocks.{i}.2''' in key]

      UpperCAmelCase													=	renew_resnet_paths(SCREAMING_SNAKE_CASE						)
      UpperCAmelCase													=	renew_resnet_paths(SCREAMING_SNAKE_CASE						)

      UpperCAmelCase													=	{'old': f'''output_blocks.{i}.0''', 'new': f'''up_blocks.{block_id}.resnets.{layer_in_block_id}'''}
      assign_to_checkpoint(
          SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]       ,   config=SCREAMING_SNAKE_CASE						)

      UpperCAmelCase													=	[key for key in resnets if 'temopral_conv' in key]
      UpperCAmelCase													=	renew_temp_conv_paths(SCREAMING_SNAKE_CASE						)
      UpperCAmelCase													=	{
          'old': f'''output_blocks.{i}.0.temopral_conv''',
          'new': f'''up_blocks.{block_id}.temp_convs.{layer_in_block_id}''',
      }
      assign_to_checkpoint(
          SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]       ,   config=SCREAMING_SNAKE_CASE						)

      UpperCAmelCase													=	{k: sorted(SCREAMING_SNAKE_CASE						) for k, v in output_block_list.items()}
      if ["conv.bias", "conv.weight"] in output_block_list.values():
        UpperCAmelCase													=	list(output_block_list.values()						).index(['conv.bias', 'conv.weight']						)
        UpperCAmelCase													=	unet_state_dict[
            f'''output_blocks.{i}.{index}.conv.weight'''
        ]
        UpperCAmelCase													=	unet_state_dict[
            f'''output_blocks.{i}.{index}.conv.bias'''
        ]

        # Clear attentions as they have been attributed above.
        if len(SCREAMING_SNAKE_CASE						) == 2:
          UpperCAmelCase													=	[]

      if len(SCREAMING_SNAKE_CASE						):
        UpperCAmelCase													=	renew_attention_paths(SCREAMING_SNAKE_CASE						)
        UpperCAmelCase													=	{
            'old': f'''output_blocks.{i}.1''',
            'new': f'''up_blocks.{block_id}.attentions.{layer_in_block_id}''',
        }
        assign_to_checkpoint(
            SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]       ,   config=SCREAMING_SNAKE_CASE						)

      if len(SCREAMING_SNAKE_CASE						):
        UpperCAmelCase													=	renew_attention_paths(SCREAMING_SNAKE_CASE						)
        UpperCAmelCase													=	{
            'old': f'''output_blocks.{i}.2''',
            'new': f'''up_blocks.{block_id}.temp_attentions.{layer_in_block_id}''',
        }
        assign_to_checkpoint(
            SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   additional_replacements=[meta_path]       ,   config=SCREAMING_SNAKE_CASE						)
    else:
      UpperCAmelCase													=	renew_resnet_paths(SCREAMING_SNAKE_CASE       ,   n_shave_prefix_segments=1						)
      for path in resnet_0_paths:
        UpperCAmelCase													=	'.'.join(['output_blocks', str(SCREAMING_SNAKE_CASE						), path['old']]						)
        UpperCAmelCase													=	'.'.join(['up_blocks', str(SCREAMING_SNAKE_CASE						), 'resnets', str(SCREAMING_SNAKE_CASE						), path['new']]						)
        UpperCAmelCase													=	unet_state_dict[old_path]

      UpperCAmelCase													=	[l for l in output_block_layers if 'temopral_conv' in l]
      for path in temopral_conv_paths:
        UpperCAmelCase													=	path.split('temopral_conv.'						)[-1]
        UpperCAmelCase													=	'.'.join(['output_blocks', str(SCREAMING_SNAKE_CASE						), str(SCREAMING_SNAKE_CASE						), 'temopral_conv', pruned_path]						)
        UpperCAmelCase													=	'.'.join(['up_blocks', str(SCREAMING_SNAKE_CASE						), 'temp_convs', str(SCREAMING_SNAKE_CASE						), pruned_path]						)
        UpperCAmelCase													=	unet_state_dict[old_path]

  return new_checkpoint


if __name__ == "__main__":
  _a				: Dict 							=						argparse.ArgumentParser()

  parser.add_argument(
      '--checkpoint_path', default=None, type=str, required=True, help='Path to the checkpoint to convert.'
  )
  parser.add_argument('--dump_path', default=None, type=str, required=True, help='Path to the output model.')
  _a				: Union[str, Any] 							=						parser.parse_args()

  _a				: Optional[int] 							=						torch.load(args.checkpoint_path, map_location='cpu')
  _a				: List[str] 							=						UNetaDConditionModel()

  _a				: Optional[int] 							=						convert_ldm_unet_checkpoint(unet_checkpoint, unet.config)

  _a				: List[str] 							=						set(unet.state_dict().keys()) - set(converted_ckpt.keys())
  _a				: Optional[Any] 							=						set(converted_ckpt.keys()) - set(unet.state_dict().keys())

  assert len(diff_a) == len(diff_a) == 0, "Converted weights don't match"

  # load state_dict
  unet.load_state_dict(converted_ckpt)

  unet.save_pretrained(args.dump_path)

  # -- finish converting the unet --





'''simple docstring'''




def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   list[list[int]]						):
  if len(SCREAMING_SNAKE_CASE						) == 0 or not all(len(SCREAMING_SNAKE_CASE						) == 2 for pair in coordinates						):
    raise ValueError('The program cannot work out a fitting polynomial.'						)

  if len({tuple(SCREAMING_SNAKE_CASE						) for pair in coordinates}						) != len(SCREAMING_SNAKE_CASE						):
    raise ValueError('The program cannot work out a fitting polynomial.'						)

  UpperCAmelCase													=	{x for x, _ in coordinates}
  if len(SCREAMING_SNAKE_CASE						) == 1:
    return f'''x={coordinates[0][0]}'''

  if len(SCREAMING_SNAKE_CASE						) != len(SCREAMING_SNAKE_CASE						):
    raise ValueError('The program cannot work out a fitting polynomial.'						)

  UpperCAmelCase													=	len(SCREAMING_SNAKE_CASE						)

  UpperCAmelCase													=	0
  UpperCAmelCase													=	[]
  # put the x and x to the power values in a matrix
  while count_of_line < x:
    UpperCAmelCase													=	0
    UpperCAmelCase													=	coordinates[count_of_line][0]
    UpperCAmelCase													=	[]
    while count_in_line < x:
      count_line.append(a ** (x - (count_in_line + 1))						)
      count_in_line += 1
    matrix.append(SCREAMING_SNAKE_CASE						)
    count_of_line += 1

  UpperCAmelCase													=	0
  # put the y values into a vector
  UpperCAmelCase													=	[]
  while count_of_line < x:
    vector.append(coordinates[count_of_line][1]						)
    count_of_line += 1

  UpperCAmelCase													=	0

  while count < x:
    UpperCAmelCase													=	0
    while zahlen < x:
      if count == zahlen:
        zahlen += 1
      if zahlen == x:
        break
      UpperCAmelCase													=	matrix[zahlen][count] / matrix[count][count]
      for counting_columns, item in enumerate(matrix[count]						):
        # manipulating all the values in the matrix
        matrix[zahlen][counting_columns] -= item * bruch
      # manipulating the values in the vector
      vector[zahlen] -= vector[count] * bruch
      zahlen += 1
    count += 1

  UpperCAmelCase													=	0
  # make solutions
  UpperCAmelCase													=	[]
  while count < x:
    solution.append(str(vector[count] / matrix[count][count]						)						)
    count += 1

  UpperCAmelCase													=	0
  UpperCAmelCase													=	'f(x)='

  while count < x:
    UpperCAmelCase													=	solution[count].split('E'						)
    if len(SCREAMING_SNAKE_CASE						) > 1:
      UpperCAmelCase													=	f'''{remove_e[0]}*10^{remove_e[1]}'''
    solved += f'''x^{x - (count + 1)}*{solution[count]}'''
    if count + 1 != x:
      solved += "+"
    count += 1

  return solved


if __name__ == "__main__":
  print(points_to_polynomial([]))
  print(points_to_polynomial([[]]))
  print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
  print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
  print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
  print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
  print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
  print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
  print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
  print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))


