"""simple docstring"""






from __future__ import annotations

from collections.abc import Callable

__lowerCAmelCase       :			Any   	=list[list[float | int]]


def      UpperCAmelCase__			(							lowerCAmelCase__	:Matrix   ,						lowerCAmelCase__	:Matrix						)					->       Matrix:
      '''simple docstring'''


      lowercase								=      len(lowerCAmelCase__						)
      lowercase								=      [[0 for _ in range(size + 1						)] for _ in range(lowerCAmelCase__						)]
      lowercase								=      42
      lowercase								=      42
      lowercase								=      42
      lowercase								=      42
      lowercase								=      42
      lowercase								=      42

      for row in range(lowerCAmelCase__						):
            for col in range(lowerCAmelCase__						):
                  lowercase								=      matrix[row][col]

            lowercase								=      vector[row][0]

      lowercase								=      0
      lowercase								=      0
      while row < size and col < size:
            # pivoting
            lowercase								=      max((abs(augmented[rowa][col]						), rowa) for rowa in range(lowerCAmelCase__   ,						lowerCAmelCase__						)						)[
                1
            ]
            if augmented[pivot_row][col] == 0:
                  col += 1
                  continue
            else:
                  lowercase				,				lowercase								=      augmented[pivot_row], augmented[row]

            for rowa in range(row + 1   ,						lowerCAmelCase__						):
                  lowercase								=      augmented[rowa][col] / augmented[row][col]
                  lowercase								=      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   ,						lowerCAmelCase__						):
            for row in range(lowerCAmelCase__						):
                  lowercase								=      augmented[row][col] / augmented[col][col]
                  for cola in range(lowerCAmelCase__   ,						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(lowerCAmelCase__						)
      ]


def      UpperCAmelCase__			(							lowerCAmelCase__	:list[int]						)					->       Callable[[int], int]:
      '''simple docstring'''


      lowercase								=      len(lowerCAmelCase__						)
      lowercase								=      [[0 for _ in range(lowerCAmelCase__						)] for _ in range(lowerCAmelCase__						)]
      lowercase								=      [[0] for _ in range(lowerCAmelCase__						)]
      lowercase								=      42
      lowercase								=      42
      lowercase								=      42
      lowercase								=      42

      for x_val, y_val in enumerate(lowerCAmelCase__						):
            for col in range(lowerCAmelCase__						):
                  lowercase								=      (x_val + 1) ** (size - col - 1)
            lowercase								=      y_val

      lowercase								=      solve(lowerCAmelCase__   ,						lowerCAmelCase__						)

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

      return interpolated_func


def      UpperCAmelCase__			(							lowerCAmelCase__	:int						)					->       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      UpperCAmelCase__			(							lowerCAmelCase__	:Callable[[int], int] = question_function   ,						lowerCAmelCase__	:int = 1_0						)					->       int:
      '''simple docstring'''


      lowercase								=      [func(lowerCAmelCase__						) for x_val in range(1   ,						order + 1						)]

      lowercase								=      [
          interpolate(data_points[:max_coeff]						) for max_coeff in range(1   ,						order + 1						)
      ]

      lowercase								=      0
      lowercase								=      42
      lowercase								=      42

      for poly in polynomials:
            lowercase								=      1
            while func(lowerCAmelCase__						) == poly(lowerCAmelCase__						):
                  x_val += 1

            ret += poly(lowerCAmelCase__						)

      return ret


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




"""simple docstring"""






import os
import unittest

from transformers.models.transfo_xl.tokenization_transfo_xl import VOCAB_FILES_NAMES, TransfoXLTokenizer

from ...test_tokenization_common import TokenizerTesterMixin





class 					_A		(			lowerCAmelCase    ,       unittest.TestCase      ):
      snake_case__     :  str				    =      TransfoXLTokenizer
      snake_case__     :  Union[str, Any]				    =      False
      snake_case__     :  Union[str, Any]				    =      False

      def 							A__			(		self		):







            """simple docstring"""



            super().setUp()

            lowercase								=      [
                """<unk>""",
                """[CLS]""",
                """[SEP]""",
                """want""",
                """unwanted""",
                """wa""",
                """un""",
                """running""",
                """,""",
                """low""",
                """l""",
            ]
            lowercase								=      os.path.join(self.tmpdirname						,			VOCAB_FILES_NAMES["""vocab_file"""]		)
            with open(self.vocab_file						,			"""w"""						,			encoding="""utf-8"""		) as vocab_writer:
                  vocab_writer.write("""""".join([x + """\n""" for x in vocab_tokens]		)		)

      def 							A__			(		self						,			**__lowerCAmelCase		):







            """simple docstring"""



            lowercase								=      True
            return TransfoXLTokenizer.from_pretrained(self.tmpdirname						,			**__lowerCAmelCase		)

      def 							A__			(		self						,			__lowerCAmelCase		):







            """simple docstring"""



            lowercase								=      """<unk> UNwanted , running"""
            lowercase								=      """<unk> unwanted, running"""
            return input_text, output_text

      def 							A__			(		self		):







            """simple docstring"""



            lowercase								=      TransfoXLTokenizer(vocab_file=self.vocab_file						,			lower_case=__lowerCAmelCase		)

            lowercase								=      tokenizer.tokenize("""<unk> UNwanted , running"""		)
            self.assertListEqual(__lowerCAmelCase						,			["""<unk>""", """unwanted""", """,""", """running"""]		)

            self.assertListEqual(tokenizer.convert_tokens_to_ids(__lowerCAmelCase		)						,			[0, 4, 8, 7]		)

      def 							A__			(		self		):







            """simple docstring"""



            lowercase								=      TransfoXLTokenizer(lower_case=__lowerCAmelCase		)

            self.assertListEqual(
                tokenizer.tokenize(""" \tHeLLo ! how  \n Are yoU ?  """		)						,			["""hello""", """!""", """how""", """are""", """you""", """?"""]		)

      def 							A__			(		self		):







            """simple docstring"""



            lowercase								=      TransfoXLTokenizer(lower_case=__lowerCAmelCase		)

            self.assertListEqual(
                tokenizer.tokenize(""" \tHeLLo ! how  \n Are yoU ?  """		)						,			["""HeLLo""", """!""", """how""", """Are""", """yoU""", """?"""]		)

      def 							A__			(		self		):







            """simple docstring"""



            lowercase								=      TransfoXLTokenizer(lower_case=__lowerCAmelCase		)
            lowercase								=      """Hello (bracket) and side-scrolled [and] Henry's $5,000 with 3.34 m. What's up!?"""
            lowercase								=      [
                """Hello""",
                """(""",
                """bracket""",
                """)""",
                """and""",
                """side""",
                """@-@""",
                """scrolled""",
                """[""",
                """and""",
                """]""",
                """Henry""",
                """'s""",
                """$""",
                """5""",
                """@,@""",
                """000""",
                """with""",
                """3""",
                """@.@""",
                """34""",
                """m""",
                """.""",
                """What""",
                """'s""",
                """up""",
                """!""",
                """?""",
            ]

            self.assertListEqual(tokenizer.tokenize(__lowerCAmelCase		)						,			__lowerCAmelCase		)

            self.assertEqual(tokenizer.convert_tokens_to_string(__lowerCAmelCase		)						,			__lowerCAmelCase		)







      def 							A__			(		self		):







            """simple docstring"""



            lowercase								=      self.get_tokenizer()
            lowercase								=      len(__lowerCAmelCase		)

            tokenizer.add_tokens(["""new1""", """new2"""]		)
            tokenizer.move_added_token("""new1"""						,			1		)

            # Check that moved token is not copied (duplicate)
            self.assertEqual(len(__lowerCAmelCase		)						,			original_len + 2		)
            # Check that token is moved to specified id
            self.assertEqual(tokenizer.encode("""new1"""		)						,			[1]		)
            self.assertEqual(tokenizer.decode([1]		)						,			"""new1"""		)



