




"""simple docstring"""

def 				a (						__snake_case     :				list[list[int]]  ):



				'''simple docstring'''





				if len(__snake_case  ) == 0 or not all(len(__snake_case  ) == 2 for pair in coordinates  ):
								raise ValueError('''The program cannot work out a fitting polynomial.'''  )

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

				UpperCAmelCase_					:Optional[Any]      			=      {x for x, _ in coordinates}
				if len(__snake_case  ) == 1:
								return f'x={coordinates[0][0]}'

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

				UpperCAmelCase_					:List[Any]      			=      len(__snake_case  )

				UpperCAmelCase_					:str      			=      0
				UpperCAmelCase_					:list[list[float]]      			=      []
				# put the x and x to the power values in a matrix
				while count_of_line < x:
								UpperCAmelCase_					:str      			=      0
								UpperCAmelCase_					:Optional[int]      			=      coordinates[count_of_line][0]
								UpperCAmelCase_					:list[float]      			=      []
								while count_in_line < x:
												count_line.append(a ** (x - (count_in_line + 1))  )
												count_in_line += 1
								matrix.append(__snake_case  )
								count_of_line += 1

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

				UpperCAmelCase_					:Dict      			=      0

				while count < x:
								UpperCAmelCase_					:Any      			=      0
								while zahlen < x:
												if count == zahlen:
																zahlen += 1
												if zahlen == x:
																break
												UpperCAmelCase_					:str      			=      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_					:Tuple      			=      0
				# make solutions
				UpperCAmelCase_					:list[str]      			=      []
				while count < x:
								solution.append(str(vector[count] / matrix[count][count]  )  )
								count += 1

				UpperCAmelCase_					:Optional[int]      			=      0
				UpperCAmelCase_					:Optional[Any]      			=      '''f(x)='''

				while count < x:
								UpperCAmelCase_					:list[str]      			=      solution[count].split('''E'''  )
								if len(__snake_case  ) > 1:
												UpperCAmelCase_					:List[Any]      			=      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]]))








"""simple docstring"""

import argparse
import json
from collections import OrderedDict
from pathlib import Path

import requests
import torch
from huggingface_hub import hf_hub_download
from PIL import Image

from transformers import DetrConfig, DetrForObjectDetection, DetrForSegmentation, DetrImageProcessor
from transformers.utils import logging


logging.set_verbosity_info()
__lowerCamelCase								=						logging.get_logger(__name__)

# here we list all keys to be renamed (original name on the left, our name on the right)
__lowerCamelCase								=						[]
for i in range(6):
						# encoder layers: output projection, 2 feedforward neural networks and 2 layernorms
						rename_keys.append(
						    (f'''transformer.encoder.layers.{i}.self_attn.out_proj.weight''', f'''encoder.layers.{i}.self_attn.out_proj.weight''')
						)
						rename_keys.append(
						    (f'''transformer.encoder.layers.{i}.self_attn.out_proj.bias''', f'''encoder.layers.{i}.self_attn.out_proj.bias''')
						)
						rename_keys.append((f'''transformer.encoder.layers.{i}.linear1.weight''', f'''encoder.layers.{i}.fc1.weight'''))
						rename_keys.append((f'''transformer.encoder.layers.{i}.linear1.bias''', f'''encoder.layers.{i}.fc1.bias'''))
						rename_keys.append((f'''transformer.encoder.layers.{i}.linear2.weight''', f'''encoder.layers.{i}.fc2.weight'''))
						rename_keys.append((f'''transformer.encoder.layers.{i}.linear2.bias''', f'''encoder.layers.{i}.fc2.bias'''))
						rename_keys.append(
						    (f'''transformer.encoder.layers.{i}.norm1.weight''', f'''encoder.layers.{i}.self_attn_layer_norm.weight''')
						)
						rename_keys.append((f'''transformer.encoder.layers.{i}.norm1.bias''', f'''encoder.layers.{i}.self_attn_layer_norm.bias'''))
						rename_keys.append((f'''transformer.encoder.layers.{i}.norm2.weight''', f'''encoder.layers.{i}.final_layer_norm.weight'''))
						rename_keys.append((f'''transformer.encoder.layers.{i}.norm2.bias''', f'''encoder.layers.{i}.final_layer_norm.bias'''))
						# decoder layers: 2 times output projection, 2 feedforward neural networks and 3 layernorms
						rename_keys.append(
						    (f'''transformer.decoder.layers.{i}.self_attn.out_proj.weight''', f'''decoder.layers.{i}.self_attn.out_proj.weight''')
						)
						rename_keys.append(
						    (f'''transformer.decoder.layers.{i}.self_attn.out_proj.bias''', f'''decoder.layers.{i}.self_attn.out_proj.bias''')
						)
						rename_keys.append(
						    (
						        f'''transformer.decoder.layers.{i}.multihead_attn.out_proj.weight''',
						        f'''decoder.layers.{i}.encoder_attn.out_proj.weight''',
						    )
						)
						rename_keys.append(
						    (
						        f'''transformer.decoder.layers.{i}.multihead_attn.out_proj.bias''',
						        f'''decoder.layers.{i}.encoder_attn.out_proj.bias''',
						    )
						)
						rename_keys.append((f'''transformer.decoder.layers.{i}.linear1.weight''', f'''decoder.layers.{i}.fc1.weight'''))
						rename_keys.append((f'''transformer.decoder.layers.{i}.linear1.bias''', f'''decoder.layers.{i}.fc1.bias'''))
						rename_keys.append((f'''transformer.decoder.layers.{i}.linear2.weight''', f'''decoder.layers.{i}.fc2.weight'''))
						rename_keys.append((f'''transformer.decoder.layers.{i}.linear2.bias''', f'''decoder.layers.{i}.fc2.bias'''))
						rename_keys.append(
						    (f'''transformer.decoder.layers.{i}.norm1.weight''', f'''decoder.layers.{i}.self_attn_layer_norm.weight''')
						)
						rename_keys.append((f'''transformer.decoder.layers.{i}.norm1.bias''', f'''decoder.layers.{i}.self_attn_layer_norm.bias'''))
						rename_keys.append(
						    (f'''transformer.decoder.layers.{i}.norm2.weight''', f'''decoder.layers.{i}.encoder_attn_layer_norm.weight''')
						)
						rename_keys.append(
						    (f'''transformer.decoder.layers.{i}.norm2.bias''', f'''decoder.layers.{i}.encoder_attn_layer_norm.bias''')
						)
						rename_keys.append((f'''transformer.decoder.layers.{i}.norm3.weight''', f'''decoder.layers.{i}.final_layer_norm.weight'''))
						rename_keys.append((f'''transformer.decoder.layers.{i}.norm3.bias''', f'''decoder.layers.{i}.final_layer_norm.bias'''))

# convolutional projection + query embeddings + layernorm of decoder + class and bounding box heads
rename_keys.extend(
    [
        ("input_proj.weight", "input_projection.weight"),
        ("input_proj.bias", "input_projection.bias"),
        ("query_embed.weight", "query_position_embeddings.weight"),
        ("transformer.decoder.norm.weight", "decoder.layernorm.weight"),
        ("transformer.decoder.norm.bias", "decoder.layernorm.bias"),
        ("class_embed.weight", "class_labels_classifier.weight"),
        ("class_embed.bias", "class_labels_classifier.bias"),
        ("bbox_embed.layers.0.weight", "bbox_predictor.layers.0.weight"),
        ("bbox_embed.layers.0.bias", "bbox_predictor.layers.0.bias"),
        ("bbox_embed.layers.1.weight", "bbox_predictor.layers.1.weight"),
        ("bbox_embed.layers.1.bias", "bbox_predictor.layers.1.bias"),
        ("bbox_embed.layers.2.weight", "bbox_predictor.layers.2.weight"),
        ("bbox_embed.layers.2.bias", "bbox_predictor.layers.2.bias"),
    ]
)



def 				a (						__snake_case     :				Optional[Any],    __snake_case     :				Any,    __snake_case     :				Tuple  ):



				'''simple docstring'''





				UpperCAmelCase_					:Optional[Any]      			=      state_dict.pop(__snake_case  )
				UpperCAmelCase_					:List[str]      			=      val



def 				a (						__snake_case     :				int  ):



				'''simple docstring'''





				UpperCAmelCase_					:int      			=      OrderedDict()
				for key, value in state_dict.items():
								if "backbone.0.body" in key:
												UpperCAmelCase_					:List[Any]      			=      key.replace('''backbone.0.body''',    '''backbone.conv_encoder.model'''  )
												UpperCAmelCase_					:Union[str, Any]      			=      value
								else:
												UpperCAmelCase_					:Any      			=      value

				return new_state_dict



def 				a (						__snake_case     :				Tuple,    __snake_case     :				Optional[Any]=False  ):



				'''simple docstring'''





				UpperCAmelCase_					:Union[str, Any]      			=      ''''''
				if is_panoptic:
								UpperCAmelCase_					:Tuple      			=      '''detr.'''

				# first: transformer encoder
				for i in range(6  ):
								# read in weights + bias of input projection layer (in PyTorch's MultiHeadAttention, this is a single matrix + bias)
								UpperCAmelCase_					:Optional[Any]      			=      state_dict.pop(f'{prefix}transformer.encoder.layers.{i}.self_attn.in_proj_weight'  )
								UpperCAmelCase_					:Tuple      			=      state_dict.pop(f'{prefix}transformer.encoder.layers.{i}.self_attn.in_proj_bias'  )
								# next, add query, keys and values (in that order) to the state dict
								UpperCAmelCase_					:List[str]      			=      in_proj_weight[:256, :]
								UpperCAmelCase_					:Union[str, Any]      			=      in_proj_bias[:256]
								UpperCAmelCase_					:List[Any]      			=      in_proj_weight[256:512, :]
								UpperCAmelCase_					:List[Any]      			=      in_proj_bias[256:512]
								UpperCAmelCase_					:str      			=      in_proj_weight[-256:, :]
								UpperCAmelCase_					:Optional[int]      			=      in_proj_bias[-256:]
				# next: transformer decoder (which is a bit more complex because it also includes cross-attention)
				for i in range(6  ):
								# read in weights + bias of input projection layer of self-attention
								UpperCAmelCase_					:List[str]      			=      state_dict.pop(f'{prefix}transformer.decoder.layers.{i}.self_attn.in_proj_weight'  )
								UpperCAmelCase_					:str      			=      state_dict.pop(f'{prefix}transformer.decoder.layers.{i}.self_attn.in_proj_bias'  )
								# next, add query, keys and values (in that order) to the state dict
								UpperCAmelCase_					:Dict      			=      in_proj_weight[:256, :]
								UpperCAmelCase_					:Optional[int]      			=      in_proj_bias[:256]
								UpperCAmelCase_					:List[Any]      			=      in_proj_weight[256:512, :]
								UpperCAmelCase_					:List[str]      			=      in_proj_bias[256:512]
								UpperCAmelCase_					:int      			=      in_proj_weight[-256:, :]
								UpperCAmelCase_					:List[str]      			=      in_proj_bias[-256:]
								# read in weights + bias of input projection layer of cross-attention
								UpperCAmelCase_					:int      			=      state_dict.pop(
								    f'{prefix}transformer.decoder.layers.{i}.multihead_attn.in_proj_weight'  )
								UpperCAmelCase_					:Optional[int]      			=      state_dict.pop(f'{prefix}transformer.decoder.layers.{i}.multihead_attn.in_proj_bias'  )
								# next, add query, keys and values (in that order) of cross-attention to the state dict
								UpperCAmelCase_					:int      			=      in_proj_weight_cross_attn[:256, :]
								UpperCAmelCase_					:str      			=      in_proj_bias_cross_attn[:256]
								UpperCAmelCase_					:Tuple      			=      in_proj_weight_cross_attn[256:512, :]
								UpperCAmelCase_					:Any      			=      in_proj_bias_cross_attn[256:512]
								UpperCAmelCase_					:str      			=      in_proj_weight_cross_attn[-256:, :]
								UpperCAmelCase_					:List[Any]      			=      in_proj_bias_cross_attn[-256:]



def 				a (						):



				'''simple docstring'''





				UpperCAmelCase_					:Tuple      			=      '''http://images.cocodataset.org/val2017/000000039769.jpg'''
				UpperCAmelCase_					:List[str]      			=      Image.open(requests.get(__snake_case,    stream=__snake_case  ).raw  )

				return im



@torch.no_grad()
def 				a (						__snake_case     :				Union[str, Any],    __snake_case     :				List[Any]  ):



				'''simple docstring'''





				UpperCAmelCase_					:Optional[int]      			=      DetrConfig()
				# set backbone and dilation attributes
				if "resnet101" in model_name:
								UpperCAmelCase_					:Optional[Any]      			=      '''resnet101'''
				if "dc5" in model_name:
								UpperCAmelCase_					:Optional[int]      			=      True
				UpperCAmelCase_					:Dict      			=      '''panoptic''' in model_name
				if is_panoptic:
								UpperCAmelCase_					:Optional[int]      			=      250
				else:
								UpperCAmelCase_					:Dict      			=      91
								UpperCAmelCase_					:Union[str, Any]      			=      '''huggingface/label-files'''
								UpperCAmelCase_					:str      			=      '''coco-detection-id2label.json'''
								UpperCAmelCase_					:Dict      			=      json.load(open(hf_hub_download(__snake_case,    __snake_case,    repo_type='''dataset'''  ),    '''r'''  )  )
								UpperCAmelCase_					:Optional[Any]      			=      {int(__snake_case  ): v for k, v in idalabel.items()}
								UpperCAmelCase_					:str      			=      idalabel
								UpperCAmelCase_					:Tuple      			=      {v: k for k, v in idalabel.items()}

				# load image processor
				UpperCAmelCase_					:Dict      			=      '''coco_panoptic''' if is_panoptic else '''coco_detection'''
				UpperCAmelCase_					:Optional[Any]      			=      DetrImageProcessor(format=__snake_case  )

				# prepare image
				UpperCAmelCase_					:Dict      			=      prepare_img()
				UpperCAmelCase_					:Union[str, Any]      			=      image_processor(images=__snake_case,    return_tensors='''pt'''  )
				UpperCAmelCase_					:Optional[Any]      			=      encoding['''pixel_values''']

				logger.info(f'Converting model {model_name}...'  )

				# load original model from torch hub
				UpperCAmelCase_					:int      			=      torch.hub.load('''facebookresearch/detr''',    __snake_case,    pretrained=__snake_case  ).eval()
				UpperCAmelCase_					:List[Any]      			=      detr.state_dict()
				# rename keys
				for src, dest in rename_keys:
								if is_panoptic:
												UpperCAmelCase_					:Optional[int]      			=      '''detr.''' + src
								rename_key(__snake_case,    __snake_case,    __snake_case  )
				UpperCAmelCase_					:int      			=      rename_backbone_keys(__snake_case  )
				# query, key and value matrices need special treatment
				read_in_q_k_v(__snake_case,    is_panoptic=__snake_case  )
				# important: we need to prepend a prefix to each of the base model keys as the head models use different attributes for them
				UpperCAmelCase_					:Tuple      			=      '''detr.model.''' if is_panoptic else '''model.'''
				for key in state_dict.copy().keys():
								if is_panoptic:
												if (
												    key.startswith('''detr'''  )
												    and not key.startswith('''class_labels_classifier'''  )
												    and not key.startswith('''bbox_predictor'''  )
												):
																UpperCAmelCase_					:List[str]      			=      state_dict.pop(__snake_case  )
																UpperCAmelCase_					:List[Any]      			=      val
												elif "class_labels_classifier" in key or "bbox_predictor" in key:
																UpperCAmelCase_					:int      			=      state_dict.pop(__snake_case  )
																UpperCAmelCase_					:Union[str, Any]      			=      val
												elif key.startswith('''bbox_attention'''  ) or key.startswith('''mask_head'''  ):
																continue
												else:
																UpperCAmelCase_					:Tuple      			=      state_dict.pop(__snake_case  )
																UpperCAmelCase_					:Dict      			=      val
								else:
												if not key.startswith('''class_labels_classifier'''  ) and not key.startswith('''bbox_predictor'''  ):
																UpperCAmelCase_					:Any      			=      state_dict.pop(__snake_case  )
																UpperCAmelCase_					:Any      			=      val
    # finally, create HuggingFace model and load state dict
				UpperCAmelCase_					:Optional[int]      			=      DetrForSegmentation(__snake_case  ) if is_panoptic else DetrForObjectDetection(__snake_case  )
				model.load_state_dict(__snake_case  )
				model.eval()
				# verify our conversion
				UpperCAmelCase_					:List[Any]      			=      detr(__snake_case  )
				UpperCAmelCase_					:Optional[int]      			=      model(__snake_case  )
				assert torch.allclose(outputs.logits,    original_outputs['''pred_logits'''],    atol=1E-4  )
				assert torch.allclose(outputs.pred_boxes,    original_outputs['''pred_boxes'''],    atol=1E-4  )
				if is_panoptic:
								assert torch.allclose(outputs.pred_masks,    original_outputs['''pred_masks'''],    atol=1E-4  )

				# Save model and image processor
				logger.info(f'Saving PyTorch model and image processor to {pytorch_dump_folder_path}...'  )
				Path(__snake_case  ).mkdir(exist_ok=__snake_case  )
				model.save_pretrained(__snake_case  )
				image_processor.save_pretrained(__snake_case  )


if __name__ == "__main__":
						__lowerCamelCase								=						argparse.ArgumentParser()

						parser.add_argument(
						    "--model_name", default="detr_resnet50", type=str, help="Name of the DETR model you'd like to convert."
						)
						parser.add_argument(
						    "--pytorch_dump_folder_path", default=None, type=str, help="Path to the folder to output PyTorch model."
						)
						__lowerCamelCase								=						parser.parse_args()
						convert_detr_checkpoint(args.model_name, args.pytorch_dump_folder_path)


