






import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch


if is_torch_available():
   import torch

   from transformers.generation import DisjunctiveConstraint



@require_torch
class 				_A			(     unittest.TestCase				):
    """simple docstring"""

    def _a							(				self      :     Tuple      )      ->							List[Any]:
           # For consistency across different places the DisjunctiveConstraint is called,
           # dc.token_ids is a list of integers. It is also initialized only by integers.

           __UpperCAmelCase     				=[[1, 2, 4], [1, 2, 3, 4]]
           __UpperCAmelCase     				=DisjunctiveConstraint(__SCREAMING_SNAKE_CASE      )
           self.assertTrue(isinstance(dc.token_ids ,     __SCREAMING_SNAKE_CASE      )      )

           with self.assertRaises(__SCREAMING_SNAKE_CASE      ):
                  DisjunctiveConstraint(torch.LongTensor([[1, 2, 4], [1, 2, 3]]      )      )

           with self.assertRaises(__SCREAMING_SNAKE_CASE      ):
                  DisjunctiveConstraint([torch.LongTensor([1, 2, 4]      ), torch.LongTensor([1, 2, 3, 4, 5]      )]      )



    def _a							(				self      :     Union[str, Any]      )      ->							Optional[Any]:
           # We can't have constraints that are complete subsets of another. This leads to a preverse
           # interpretation of "constraint fulfillment": does generating [1,2,3] fulfill the constraint?
           # It would mean that it generated [1,2] which fulfills it, but it's in the middle of potentially
           # fulfilling [1,2,3,4]. If we believe that [1,2,3] does fulfill the constraint, then the algorithm
           # will necessarily never reach [1,2,3,4], giving users a false sense of control (better to just not allow it).
           __UpperCAmelCase     				=[[1, 2], [1, 2, 3, 4]]

           with self.assertRaises(__SCREAMING_SNAKE_CASE      ):
                  DisjunctiveConstraint(__SCREAMING_SNAKE_CASE      )  # fails here



    def _a							(				self      :     int      )      ->							Tuple:
           __UpperCAmelCase     				=[[1, 2, 3], [1, 2, 4]]

           __UpperCAmelCase     				=DisjunctiveConstraint(__SCREAMING_SNAKE_CASE      )

           __UpperCAmelCase				, __UpperCAmelCase				, __UpperCAmelCase     				=dc.update(1      )
           __UpperCAmelCase     				=stepped is True and completed is False and reset is False
           self.assertTrue(__SCREAMING_SNAKE_CASE      )
           self.assertTrue(not dc.completed      )
           self.assertTrue(dc.current_seq == [1]      )

           __UpperCAmelCase				, __UpperCAmelCase				, __UpperCAmelCase     				=dc.update(2      )
           __UpperCAmelCase     				=stepped is True and completed is False and reset is False
           self.assertTrue(__SCREAMING_SNAKE_CASE      )
           self.assertTrue(not dc.completed      )
           self.assertTrue(dc.current_seq == [1, 2]      )

           __UpperCAmelCase				, __UpperCAmelCase				, __UpperCAmelCase     				=dc.update(3      )
           __UpperCAmelCase     				=stepped is True and completed is True and reset is False
           self.assertTrue(__SCREAMING_SNAKE_CASE      )
           self.assertTrue(dc.completed      )  # Completed!
           self.assertTrue(dc.current_seq == [1, 2, 3]      )



    def _a							(				self      :     Optional[Any]      )      ->							Optional[int]:
           __UpperCAmelCase     				=[[1, 2, 3], [1, 2, 4, 5], [1, 2, 5]]

           __UpperCAmelCase     				=DisjunctiveConstraint(__SCREAMING_SNAKE_CASE      )

           __UpperCAmelCase				, __UpperCAmelCase				, __UpperCAmelCase     				=dc.update(1      )
           self.assertTrue(not dc.completed      )
           self.assertTrue(dc.current_seq == [1]      )

           __UpperCAmelCase				, __UpperCAmelCase				, __UpperCAmelCase     				=dc.update(2      )
           self.assertTrue(not dc.completed      )
           self.assertTrue(dc.current_seq == [1, 2]      )

           __UpperCAmelCase				, __UpperCAmelCase				, __UpperCAmelCase     				=dc.update(4      )
           self.assertTrue(not dc.completed      )
           self.assertTrue(dc.current_seq == [1, 2, 4]      )

           __UpperCAmelCase				, __UpperCAmelCase				, __UpperCAmelCase     				=dc.update(5      )
           self.assertTrue(dc.completed      )  # Completed!
           self.assertTrue(dc.current_seq == [1, 2, 4, 5]      )

           dc.reset()

           __UpperCAmelCase				, __UpperCAmelCase				, __UpperCAmelCase     				=dc.update(1      )
           self.assertTrue(not dc.completed      )
           self.assertTrue(dc.remaining() == 3      )
           self.assertTrue(dc.current_seq == [1]      )

           __UpperCAmelCase				, __UpperCAmelCase				, __UpperCAmelCase     				=dc.update(2      )
           self.assertTrue(not dc.completed      )
           self.assertTrue(dc.remaining() == 2      )
           self.assertTrue(dc.current_seq == [1, 2]      )

           __UpperCAmelCase				, __UpperCAmelCase				, __UpperCAmelCase     				=dc.update(5      )
           self.assertTrue(dc.completed      )  # Completed!
           self.assertTrue(dc.remaining() == 0      )
           self.assertTrue(dc.current_seq == [1, 2, 5]      )









from __future__ import annotations

from fractions import Fraction


def A    (							__UpperCamelCase			,						__UpperCamelCase       )    ->   bool:
			return (
			    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
			)


def A    (							__UpperCamelCase       )    ->   list[str]:
			A__	  =     []
			A__	  =     11
			A__	  =     int('1' + '0' * digit_len       )
			for num in range(__UpperCamelCase			,						__UpperCamelCase       ):
						while den <= 99:
									if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
												if is_digit_cancelling(__UpperCamelCase			,						__UpperCamelCase       ):
															solutions.append(f'''{num}/{den}'''       )
									den += 1
						num += 1
						A__	  =     10
			return solutions


def A    (							__UpperCamelCase = 2       )    ->   int:
			A__	  =     1.0
			for fraction in fraction_list(__UpperCamelCase       ):
						A__	  =     Fraction(__UpperCamelCase       )
						result *= frac.denominator / frac.numerator
			return int(__UpperCamelCase       )


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




