






from __future__ import annotations






def   a      (						lowerCamelCase_    ):






				'''simple docstring'''
				lowercase__       			=      [0] * max_one

				for i in range(0		,       lowerCamelCase_    ):
								lowercase__       			=      i

				for i in range(2		,       lowerCamelCase_    ):
								if totients[i] == i:
												for j in range(lowerCamelCase_		,       lowerCamelCase_		,       lowerCamelCase_    ):
																totients[j] -= totients[j] // i

				return totients






def   a      (						lowerCamelCase_		,       lowerCamelCase_    ):






				'''simple docstring'''
				return sorted(str(lowerCamelCase_    )    ) == sorted(str(lowerCamelCase_    )    )






def   a      (						lowerCamelCase_ = 1000_0000    ):






				'''simple docstring'''
				lowercase__       			=      1  # i
				lowercase__       			=      0  # φ(i)
				lowercase__       			=      get_totients(max_n + 1    )

				for i in range(2		,       max_n + 1    ):
								lowercase__       			=      totients[i]

								if i * min_denominator < min_numerator * t and has_same_digits(lowerCamelCase_		,       lowerCamelCase_    ):
												lowercase__       			=      i
												lowercase__       			=      t

				return min_numerator


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










import unittest

from datasets import load_dataset

from transformers import load_tool

from .test_tools_common import ToolTesterMixin
class 				_UpperCAmelCase (	unittest.TestCase		,A__     ):

				"""simple docstring"""




				def     lowercase__       (					self						:   str  ):

								'''simple docstring'''
								lowercase__       			=      load_tool('''document-question-answering'''  )
								self.tool.setup()
								lowercase__       			=      load_tool('''document-question-answering''',  remote=lowerCamelCase  )




				def     lowercase__       (					self						:   List[Any]  ):

								'''simple docstring'''
								lowercase__       			=      load_dataset('''hf-internal-testing/example-documents''',  split='''test'''  )
								lowercase__       			=      dataset[0]['''image''']

								lowercase__       			=      self.tool(lowerCamelCase,  '''When is the coffee break?'''  )
								self.assertEqual(lowerCamelCase,  '''11-14 to 11:39 a.m.'''  )




				def     lowercase__       (					self						:   Optional[Any]  ):

								'''simple docstring'''
								lowercase__       			=      load_dataset('''hf-internal-testing/example-documents''',  split='''test'''  )
								lowercase__       			=      dataset[0]['''image''']

								lowercase__       			=      self.remote_tool(lowerCamelCase,  '''When is the coffee break?'''  )
								self.assertEqual(lowerCamelCase,  '''11-14 to 11:39 a.m.'''  )




				def     lowercase__       (					self						:   Any  ):

								'''simple docstring'''
								lowercase__       			=      load_dataset('''hf-internal-testing/example-documents''',  split='''test'''  )
								lowercase__       			=      dataset[0]['''image''']

								self.tool(document=lowerCamelCase,  question='''When is the coffee break?'''  )




				def     lowercase__       (					self						:   Tuple  ):

								'''simple docstring'''
								lowercase__       			=      load_dataset('''hf-internal-testing/example-documents''',  split='''test'''  )
								lowercase__       			=      dataset[0]['''image''']

								lowercase__       			=      self.remote_tool(document=lowerCamelCase,  question='''When is the coffee break?'''  )
								self.assertEqual(lowerCamelCase,  '''11-14 to 11:39 a.m.'''  )




