






'''simple docstring'''
import unittest

from transformers import JukeboxTokenizer
from transformers.testing_utils import require_torch






class      __SCREAMING_SNAKE_CASE      (			unittest.TestCase				):
 snake_case_  							=							JukeboxTokenizer
 snake_case_  							=							{
     """artist""": """Zac Brown Band""",
     """genres""": """Country""",
     """lyrics""": """I met a traveller from an antique land,
        Who said \"Two vast and trunkless legs of stone
        Stand in the desert. . . . Near them, on the sand,
        Half sunk a shattered visage lies, whose frown,
        And wrinkled lip, and sneer of cold command,
        Tell that its sculptor well those passions read
        Which yet survive, stamped on these lifeless things,
        The hand that mocked them, and the heart that fed;
        And on the pedestal, these words appear:
        My name is Ozymandias, King of Kings;
        Look on my Works, ye Mighty, and despair!
        Nothing beside remains. Round the decay
        Of that colossal Wreck, boundless and bare
        The lone and level sands stretch far away
        """,
 }




 @require_torch
 def      __magic_name__	(      self	:							Optional[int]      )	->						str:
       import torch

       SCREAMING_SNAKE_CASE__     :				List[str]									=JukeboxTokenizer.from_pretrained('''openai/jukebox-1b-lyrics'''      )
       SCREAMING_SNAKE_CASE__     :				str									=tokenizer(**self.metas      )['''input_ids''']
       # fmt: off
       SCREAMING_SNAKE_CASE__     :				str									=[
           torch.tensor([[
               0, 0, 0, 71_69, 5_07, 9, 76, 39, 31, 46, 76, 27,
               76, 46, 44, 27, 48, 31, 38, 38, 31, 44, 76, 32,
               44, 41, 39, 76, 27, 40, 76, 27, 40, 46, 35, 43,
               47, 31, 76, 38, 27, 40, 30, 64, 78, 76, 76, 76,
               76, 76, 76, 76, 76, 23, 34, 41, 76, 45, 27, 35,
               30, 76, 71, 20, 49, 41, 76, 48, 27, 45, 46, 76,
               27, 40, 30, 76, 46, 44, 47, 40, 37, 38, 31, 45,
               45, 76, 38, 31, 33, 45, 76, 41, 32, 76, 45, 46,
               41, 40, 31, 78, 76, 76, 76, 76, 76, 76, 76, 76,
               19, 46, 27, 40, 30, 76, 35, 40, 76, 46, 34, 31,
               76, 30, 31, 45, 31, 44, 46, 63, 76, 63, 76, 63,
               76, 63, 76, 14, 31, 27, 44, 76, 46, 34, 31, 39,
               64, 76, 41, 40, 76, 46, 34, 31, 76, 45, 27, 40,
               30, 64, 78, 76, 76, 76, 76, 76, 76, 76, 76, 8,
               27, 38, 32, 76, 45, 47, 40, 37, 76, 27, 76, 45,
               34, 27, 46, 46, 31, 44, 31, 30, 76, 48, 35, 45,
               27, 33, 31, 76, 38, 35, 31, 45, 64, 76, 49, 34,
               41, 45, 31, 76, 32, 44, 41, 49, 40, 64, 78, 76,
               76, 76, 76, 76, 76, 76, 76, 1, 40, 30, 76, 49,
               44, 35, 40, 37, 38, 31, 30, 76, 38, 35, 42, 64,
               76, 27, 40, 30, 76, 45, 40, 31, 31, 44, 76, 41,
               32, 76, 29, 41, 38, 30, 76, 29, 41, 39, 39, 27,
               40, 30, 64, 78, 76, 76, 76, 76, 76, 76, 76, 76,
               20, 31, 38, 38, 76, 46, 34, 27, 46, 76, 35, 46,
               45, 76, 45, 29, 47, 38, 42, 46, 41, 44, 76, 49,
               31, 38, 38, 76, 46, 34, 41, 45, 31, 76, 42, 27,
               45, 45, 35, 41, 40, 45, 76, 44, 31, 27, 30, 78,
               76, 76, 76, 76, 76, 76, 76, 76, 23, 34, 35, 29,
               34, 76, 51, 31, 46, 76, 45, 47, 44, 48, 35, 48,
               31, 64, 76, 45, 46, 27, 39, 42, 31, 30, 76, 41,
               40, 76, 46, 34, 31, 45, 31, 76, 38, 35, 32, 31,
               38, 31, 45, 45, 76, 46, 34, 35, 40, 33, 45, 64,
               78, 76, 76, 76, 76, 76, 76, 76, 76, 20, 34, 31,
               76, 34, 27, 40, 30, 76, 46, 34, 27, 46, 76, 39,
               41, 29, 37, 31, 30, 76, 46, 34, 31, 39, 64, 76,
               27, 40, 30, 76, 46, 34, 31, 76, 34, 31, 27, 44,
               46, 76, 46, 34, 27, 46, 76, 32, 31, 30, 66, 78,
               76, 76, 76, 76, 76, 76, 76, 76, 1, 40, 30, 76,
               41, 40, 76, 46, 34, 31, 76, 42, 31, 30, 31, 45,
               46, 27, 38, 64, 76, 46, 34, 31, 45, 31, 76, 49,
               41, 44, 30, 45, 76, 27, 42, 42, 31, 27, 44, 65,
               78, 76, 76, 76, 76, 76, 76, 76, 76, 13, 51, 76,
               40, 27, 39, 31, 76, 35, 45, 76, 15, 52, 51, 39,
               27, 40, 30, 35, 27, 45, 64, 76, 11, 35, 40, 33,
               76, 41, 32, 76, 11, 35, 40, 33, 45, 66, 78, 76,
               76, 76, 76, 76, 76, 76, 76, 12, 41, 41, 37, 76,
               41, 40, 76, 39, 51, 76, 23, 41, 44, 37, 45, 64,
               76, 51, 31, 76, 13, 35, 33, 34, 46, 51, 64, 76,
               27, 40, 30, 76, 30, 31, 45, 42, 27, 35, 44, 67,
               78, 76, 76, 76, 76, 76, 76, 76, 76, 14, 41, 46,
               34, 35, 40, 33, 76, 28, 31, 45, 35, 30, 31, 76,
               44, 31, 39, 27, 35, 40, 45, 63, 76, 18, 41, 47,
               40, 30, 76, 46, 34, 31, 76, 30, 31, 29, 27, 51,
               78, 76, 76, 76, 76, 76, 76, 76, 76, 15, 32, 76,
               46, 34, 27, 46, 76, 29, 41, 38, 41, 45, 45, 27,
               38, 76, 23, 44, 31, 29, 37, 64, 76, 28, 41, 47,
               40, 30, 38, 31, 45, 45, 76, 27, 40, 30, 76, 28,
               27, 44, 31, 78, 76, 76, 76, 76, 76, 76, 76, 76,
               20, 34, 31, 76, 38, 41, 40, 31, 76, 27, 40, 30,
               76, 38, 31, 48, 31, 38, 76, 45, 27, 40, 30, 45,
               76, 45, 46, 44, 31, 46, 29, 34, 76, 32, 27, 44,
               76, 27, 49, 27, 51, 78, 76, 76, 76, 76, 76, 76,
               76, 76]]      ),
           torch.tensor([[0, 0, 0, 10_69, 11]]      ),
           torch.tensor([[0, 0, 0, 10_69, 11]]      ),
       ]
       # fmt: on
       self.assertTrue(torch.allclose(tokens[0]					,      EXPECTED_OUTPUT[0]      )      )
       self.assertTrue(torch.allclose(tokens[1]					,      EXPECTED_OUTPUT[1]      )      )
       self.assertTrue(torch.allclose(tokens[2]					,      EXPECTED_OUTPUT[2]      )      )




 @require_torch
 def      __magic_name__	(      self	:							Any      )	->						List[str]:
       import torch

       SCREAMING_SNAKE_CASE__     :				int									=JukeboxTokenizer.from_pretrained('''openai/jukebox-5b-lyrics'''      )
       SCREAMING_SNAKE_CASE__     :				List[str]									=tokenizer(**self.metas      )['''input_ids''']
       # fmt: off
       SCREAMING_SNAKE_CASE__     :				Optional[int]									=[
           torch.tensor([[
               0, 0, 0, 10_69, 11, -1, -1, -1, -1, 9, 77, 39,
               31, 46, 77, 27, 77, 46, 44, 27, 48, 31, 38, 38,
               31, 44, 77, 32, 44, 41, 39, 77, 27, 40, 77, 27,
               40, 46, 35, 43, 47, 31, 77, 38, 27, 40, 30, 64,
               79, 77, 77, 77, 77, 77, 77, 77, 77, 23, 34, 41,
               77, 45, 27, 35, 30, 77, 72, 20, 49, 41, 77, 48,
               27, 45, 46, 77, 27, 40, 30, 77, 46, 44, 47, 40,
               37, 38, 31, 45, 45, 77, 38, 31, 33, 45, 77, 41,
               32, 77, 45, 46, 41, 40, 31, 79, 77, 77, 77, 77,
               77, 77, 77, 77, 19, 46, 27, 40, 30, 77, 35, 40,
               77, 46, 34, 31, 77, 30, 31, 45, 31, 44, 46, 63,
               77, 63, 77, 63, 77, 63, 77, 14, 31, 27, 44, 77,
               46, 34, 31, 39, 64, 77, 41, 40, 77, 46, 34, 31,
               77, 45, 27, 40, 30, 64, 79, 77, 77, 77, 77, 77,
               77, 77, 77, 8, 27, 38, 32, 77, 45, 47, 40, 37,
               77, 27, 77, 45, 34, 27, 46, 46, 31, 44, 31, 30,
               77, 48, 35, 45, 27, 33, 31, 77, 38, 35, 31, 45,
               64, 77, 49, 34, 41, 45, 31, 77, 32, 44, 41, 49,
               40, 64, 79, 77, 77, 77, 77, 77, 77, 77, 77, 1,
               40, 30, 77, 49, 44, 35, 40, 37, 38, 31, 30, 77,
               38, 35, 42, 64, 77, 27, 40, 30, 77, 45, 40, 31,
               31, 44, 77, 41, 32, 77, 29, 41, 38, 30, 77, 29,
               41, 39, 39, 27, 40, 30, 64, 79, 77, 77, 77, 77,
               77, 77, 77, 77, 20, 31, 38, 38, 77, 46, 34, 27,
               46, 77, 35, 46, 45, 77, 45, 29, 47, 38, 42, 46,
               41, 44, 77, 49, 31, 38, 38, 77, 46, 34, 41, 45,
               31, 77, 42, 27, 45, 45, 35, 41, 40, 45, 77, 44,
               31, 27, 30, 79, 77, 77, 77, 77, 77, 77, 77, 77,
               23, 34, 35, 29, 34, 77, 51, 31, 46, 77, 45, 47,
               44, 48, 35, 48, 31, 64, 77, 45, 46, 27, 39, 42,
               31, 30, 77, 41, 40, 77, 46, 34, 31, 45, 31, 77,
               38, 35, 32, 31, 38, 31, 45, 45, 77, 46, 34, 35,
               40, 33, 45, 64, 79, 77, 77, 77, 77, 77, 77, 77,
               77, 20, 34, 31, 77, 34, 27, 40, 30, 77, 46, 34,
               27, 46, 77, 39, 41, 29, 37, 31, 30, 77, 46, 34,
               31, 39, 64, 77, 27, 40, 30, 77, 46, 34, 31, 77,
               34, 31, 27, 44, 46, 77, 46, 34, 27, 46, 77, 32,
               31, 30, 66, 79, 77, 77, 77, 77, 77, 77, 77, 77,
               1, 40, 30, 77, 41, 40, 77, 46, 34, 31, 77, 42,
               31, 30, 31, 45, 46, 27, 38, 64, 77, 46, 34, 31,
               45, 31, 77, 49, 41, 44, 30, 45, 77, 27, 42, 42,
               31, 27, 44, 65, 79, 77, 77, 77, 77, 77, 77, 77,
               77, 13, 51, 77, 40, 27, 39, 31, 77, 35, 45, 77,
               15, 52, 51, 39, 27, 40, 30, 35, 27, 45, 64, 77,
               11, 35, 40, 33, 77, 41, 32, 77, 11, 35, 40, 33,
               45, 66, 79, 77, 77, 77, 77, 77, 77, 77, 77, 12,
               41, 41, 37, 77, 41, 40, 77, 39, 51, 77, 23, 41,
               44, 37, 45, 64, 77, 51, 31, 77, 13, 35, 33, 34,
               46, 51, 64, 77, 27, 40, 30, 77, 30, 31, 45, 42,
               27, 35, 44, 67, 79, 77, 77, 77, 77, 77, 77, 77,
               77, 14, 41, 46, 34, 35, 40, 33, 77, 28, 31, 45,
               35, 30, 31, 77, 44, 31, 39, 27, 35, 40, 45, 63,
               77, 18, 41, 47, 40, 30, 77, 46, 34, 31, 77, 30,
               31, 29, 27, 51, 79, 77, 77, 77, 77, 77, 77, 77,
               77, 15, 32, 77, 46, 34, 27, 46, 77, 29, 41, 38,
               41, 45, 45, 27, 38, 77, 23, 44, 31, 29, 37, 64,
               77, 28, 41, 47, 40, 30, 38, 31, 45, 45, 77, 27,
               40, 30, 77, 28, 27, 44, 31, 79, 77, 77, 77, 77,
               77, 77, 77, 77, 20, 34, 31, 77, 38, 41, 40, 31,
               77, 27, 40, 30, 77, 38, 31, 48, 31, 38, 77, 45,
               27, 40, 30, 45, 77, 45, 46, 44, 31, 46, 29, 34,
               77, 32, 27, 44, 77, 27, 49, 27, 51, 79, 77, 77,
               77, 77, 77, 77, 77, 77]]      ),
           torch.tensor([[0, 0, 0, 10_69, 11, -1, -1, -1, -1]]      ),
           torch.tensor([[0, 0, 0, 10_69, 11, -1, -1, -1, -1]]      ),
       ]
       # fmt: on
       self.assertTrue(torch.allclose(tokens[0]					,      EXPECTED_OUTPUT[0]      )      )
       self.assertTrue(torch.allclose(tokens[1]					,      EXPECTED_OUTPUT[1]      )      )
       self.assertTrue(torch.allclose(tokens[2]					,      EXPECTED_OUTPUT[2]      )      )







'''simple docstring'''
from __future__ import annotations

from collections.abc import Callable

a_					= list[list[float | int]]





def  _a(  UpperCamelCase__				:						Matrix,	UpperCamelCase__				:						Matrix							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				int									=len(UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0 for _ in range(size + 1							)] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				float

      for row in range(UpperCamelCase__							):
            for col in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Tuple									=matrix[row][col]

            SCREAMING_SNAKE_CASE__     :				Optional[int]									=vector[row][0]

      SCREAMING_SNAKE_CASE__     :				Any									=0
      SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=0
      while row < size and col < size:
            # pivoting
            SCREAMING_SNAKE_CASE__     :				Any									=max((abs(augmented[rowa][col]							), rowa) for rowa in range(UpperCamelCase__,	UpperCamelCase__							)							)[
                1
            ]
            if augmented[pivot_row][col] == 0:
                  col += 1
                  continue
            else:
                  SCREAMING_SNAKE_CASE__		,	SCREAMING_SNAKE_CASE__     :				Optional[Any]									=augmented[pivot_row], augmented[row]

            for rowa in range(row + 1,	UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=augmented[rowa][col] / augmented[row][col]
                  SCREAMING_SNAKE_CASE__     :				Tuple									=0
                  for cola in range(col + 1,	size + 1							):
                        augmented[rowa][cola] -= augmented[row][cola] * ratio

            row += 1
            col += 1

      # back substitution
      for col in range(1,	UpperCamelCase__							):
            for row in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Optional[Any]									=augmented[row][col] / augmented[col][col]
                  for cola in range(UpperCamelCase__,	size + 1							):
                        augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
      return [
          [round(augmented[row][size] / augmented[row][row],	1_0							)] for row in range(UpperCamelCase__							)
      ]





def  _a(  UpperCamelCase__				:						list[int]							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				int									=len(UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0 for _ in range(UpperCamelCase__							)] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				Matrix
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int

      for x_val, y_val in enumerate(UpperCamelCase__							):
            for col in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Optional[int]									=(x_val + 1) ** (size - col - 1)
            SCREAMING_SNAKE_CASE__     :				Dict									=y_val

      SCREAMING_SNAKE_CASE__     :				Optional[int]									=solve(UpperCamelCase__,	UpperCamelCase__							)

      def interpolated_func(UpperCamelCase__				:						int							) -> int:
            return sum(
                round(coeffs[x_val][0]							) * (var ** (size - x_val - 1))
                for x_val in range(UpperCamelCase__							)							)

      return interpolated_func





def  _a(  UpperCamelCase__				:						int							):




      '''simple docstring'''






      return (
          1
          - variable
          + variable**2
          - variable**3
          + variable**4
          - variable**5
          + variable**6
          - variable**7
          + variable**8
          - variable**9
          + variable**1_0
      )





def  _a(  UpperCamelCase__				:						Callable[[int], int] = question_function,	UpperCamelCase__				:						int = 1_0							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				list[int]									=[func(UpperCamelCase__							) for x_val in range(1,	order + 1							)]

      SCREAMING_SNAKE_CASE__     :				list[Callable[[int], int]]									=[
          interpolate(data_points[:max_coeff]							) for max_coeff in range(1,	order + 1							)
      ]

      SCREAMING_SNAKE_CASE__     :				int									=0
      SCREAMING_SNAKE_CASE__     :				Callable[[int], int]
      SCREAMING_SNAKE_CASE__     :				int

      for poly in polynomials:
            SCREAMING_SNAKE_CASE__     :				Any									=1
            while func(UpperCamelCase__							) == poly(UpperCamelCase__							):
                  x_val += 1

            ret += poly(UpperCamelCase__							)

      return ret


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