




import argparse
from collections import defaultdict

import yaml


UpperCamelCase__    			=			"""docs/source/en/_toctree.yml"""







def 	_a      (						SCREAMING_SNAKE_CASE_							:				List[str]     ):
					__lowerCAmelCase				   =       defaultdict(SCREAMING_SNAKE_CASE_     )
					for doc in model_doc:
										counts[doc["local"]] += 1
					__lowerCAmelCase				   =       [key for key, value in counts.items() if value > 1]

					__lowerCAmelCase				   =       []
					for duplicate_key in duplicates:
										__lowerCAmelCase				   =       list({doc["title"] for doc in model_doc if doc["local"] == duplicate_key}     )
										if len(SCREAMING_SNAKE_CASE_     ) > 1:
															raise ValueError(
															    F"""{duplicate_key} is present several times in the documentation table of content at """
															    "`docs/source/en/_toctree.yml` with different *Title* values. Choose one of those and remove the "
															    "others."     )
										# Only add this once
										new_doc.append({"local": duplicate_key, "title": titles[0]}     )

					# Add none duplicate-keys
					new_doc.extend([doc for doc in model_doc if counts[doc["local"]] == 1]     )

					# Sort
					return sorted(SCREAMING_SNAKE_CASE_      ,      key=lambda SCREAMING_SNAKE_CASE_     : s["title"].lower()     )







def 	_a      (						SCREAMING_SNAKE_CASE_							:				Tuple=False     ):
					with open(SCREAMING_SNAKE_CASE_      ,      encoding="utf-8"     ) as f:
										__lowerCAmelCase				   =       yaml.safe_load(f.read()     )

					# Get to the API doc
					__lowerCAmelCase				   =       0
					while content[api_idx]["title"] != "API":
										api_idx += 1
					__lowerCAmelCase				   =       content[api_idx]["sections"]

					# Then to the model doc
					__lowerCAmelCase				   =       0
					while api_doc[model_idx]["title"] != "Models":
										model_idx += 1

					__lowerCAmelCase				   =       api_doc[model_idx]["sections"]

					__lowerCAmelCase				   =       [(idx, section) for idx, section in enumerate(SCREAMING_SNAKE_CASE_     ) if "sections" in section]
					__lowerCAmelCase				   =       False
					for idx, modality_doc in modalities_docs:
										__lowerCAmelCase				   =       modality_doc["sections"]
										__lowerCAmelCase				   =       clean_model_doc_toc(SCREAMING_SNAKE_CASE_     )

										if old_modality_doc != new_modality_doc:
															__lowerCAmelCase				   =       True
															if overwrite:
																				__lowerCAmelCase				   =       new_modality_doc

					if diff:
										if overwrite:
															__lowerCAmelCase				   =       model_doc
															__lowerCAmelCase				   =       api_doc
															with open(SCREAMING_SNAKE_CASE_      ,      "w"      ,      encoding="utf-8"     ) as f:
																				f.write(yaml.dump(SCREAMING_SNAKE_CASE_      ,      allow_unicode=SCREAMING_SNAKE_CASE_     )     )
										else:
															raise ValueError(
															    "The model doc part of the table of content is not properly sorted, run `make style` to fix this."     )


if __name__ == "__main__":
					UpperCamelCase__    			=			argparse.ArgumentParser()
					parser.add_argument("""--fix_and_overwrite""", action="""store_true""", help="""Whether to fix inconsistencies.""")
					UpperCamelCase__    			=			parser.parse_args()

					check_model_doc(args.fix_and_overwrite)










def 	_a      (						SCREAMING_SNAKE_CASE_							:				int = 1_00_00_00     ):
					__lowerCAmelCase				   =       [i - 1 for i in range(limit + 1     )]

					for i in range(2      ,      limit + 1     ):
										if phi[i] == i - 1:
															for j in range(2 * i      ,      limit + 1      ,      SCREAMING_SNAKE_CASE_     ):
																				phi[j] -= phi[j] // i

					return sum(phi[2 : limit + 1]     )


if __name__ == "__main__":
					print(solution())




