

from __future__ import annotations

from collections.abc import Callable

a_     :    List[str]     		=   list[list[float | int]]


def 							__lowerCAmelCase     (							_UpperCamelCase		:	Matrix		,				_UpperCamelCase		:	Matrix						)		->				Matrix:
 '''simple docstring'''


 SCREAMING_SNAKE_CASE		    =      len(_UpperCamelCase						)
 SCREAMING_SNAKE_CASE		    =      [[0 for _ in range(size + 1						)] for _ in range(_UpperCamelCase						)]
 SCREAMING_SNAKE_CASE		    =      42
 SCREAMING_SNAKE_CASE		    =      42
 SCREAMING_SNAKE_CASE		    =      42
 SCREAMING_SNAKE_CASE		    =      42
 SCREAMING_SNAKE_CASE		    =      42
 SCREAMING_SNAKE_CASE		    =      42

 for row in range(_UpperCamelCase						):
  for col in range(_UpperCamelCase						):
   SCREAMING_SNAKE_CASE		    =      matrix[row][col]

  SCREAMING_SNAKE_CASE		    =      vector[row][0]

 SCREAMING_SNAKE_CASE		    =      0
 SCREAMING_SNAKE_CASE		    =      0
 while row < size and col < size:
  # pivoting
  SCREAMING_SNAKE_CASE		    =      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		    =      augmented[pivot_row], augmented[row]

  for rowa in range(row + 1		,				_UpperCamelCase						):
   SCREAMING_SNAKE_CASE		    =      augmented[rowa][col] / augmented[row][col]
   SCREAMING_SNAKE_CASE		    =      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		    =      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]		,				10						)] for row in range(_UpperCamelCase						)
 ]


def 							__lowerCAmelCase     (							_UpperCamelCase		:	list[int]						)		->				Callable[[int], int]:
 '''simple docstring'''


 SCREAMING_SNAKE_CASE		    =      len(_UpperCamelCase						)
 SCREAMING_SNAKE_CASE		    =      [[0 for _ in range(_UpperCamelCase						)] for _ in range(_UpperCamelCase						)]
 SCREAMING_SNAKE_CASE		    =      [[0] for _ in range(_UpperCamelCase						)]
 SCREAMING_SNAKE_CASE		    =      42
 SCREAMING_SNAKE_CASE		    =      42
 SCREAMING_SNAKE_CASE		    =      42
 SCREAMING_SNAKE_CASE		    =      42

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

 SCREAMING_SNAKE_CASE		    =      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 							__lowerCAmelCase     (							_UpperCamelCase		:	int						)		->				int:
 '''simple docstring'''


 return (
     1
     - variable
     + variable**2
     - variable**3
     + variable**4
     - variable**5
     + variable**6
     - variable**7
     + variable**8
     - variable**9
     + variable**10
 )


def 							__lowerCAmelCase     (							_UpperCamelCase		:	Callable[[int], int] = question_function		,				_UpperCamelCase		:	int = 10						)		->				int:
 '''simple docstring'''


 SCREAMING_SNAKE_CASE		    =      [func(_UpperCamelCase						) for x_val in range(1		,				order + 1						)]

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

 SCREAMING_SNAKE_CASE		    =      0
 SCREAMING_SNAKE_CASE		    =      42
 SCREAMING_SNAKE_CASE		    =      42

 for poly in polynomials:
  SCREAMING_SNAKE_CASE		    =      1
  while func(_UpperCamelCase						) == poly(_UpperCamelCase						):
   x_val += 1

  ret += poly(_UpperCamelCase						)

 return ret


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




import string


def 							__lowerCAmelCase     (							_UpperCamelCase		:	str						)		->				str:
 '''simple docstring'''


 SCREAMING_SNAKE_CASE		    =      ''
 for i in sequence:
  SCREAMING_SNAKE_CASE		    =      ord(_UpperCamelCase						)
  if 65 <= extract <= 90:
   output += chr(1_55 - extract						)
  elif 97 <= extract <= 1_22:
   output += chr(2_19 - extract						)
  else:
   output += i
 return output


def 							__lowerCAmelCase     (							_UpperCamelCase		:	str						)		->				str:
 '''simple docstring'''


 SCREAMING_SNAKE_CASE		    =      string.ascii_letters
 SCREAMING_SNAKE_CASE		    =      string.ascii_lowercase[::-1] + string.ascii_uppercase[::-1]
 return "".join(
     letters_reversed[letters.index(_UpperCamelCase						)] if c in letters else c for c in sequence						)


def 							__lowerCAmelCase     (							)		->				None:
 '''simple docstring'''


 from timeit import timeit

 print('Running performance benchmarks...'						)
 SCREAMING_SNAKE_CASE		    =      'from string import printable ; from __main__ import atbash, atbash_slow'
 print(f"""> atbash_slow(): {timeit('atbash_slow(printable)'		,				setup=_UpperCamelCase						)} seconds"""						)
 print(f""">      atbash(): {timeit('atbash(printable)'		,				setup=_UpperCamelCase						)} seconds"""						)


if __name__ == "__main__":
      for example in ("ABCDEFGH", "123GGjj", "testStringtest", "with space"):
            print(F"""{example} encrypted in atbash: {atbash(example)}""")
      benchmark()

