
'''simple docstring'''



from __future__ import annotations

from collections.abc import Callable

UpperCamelCase__      :		Optional[Any]       							=  list[list[float | int]]
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)     ->     Matrix:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE      =				len(SCREAMING_SNAKE_CASE_						)
   _SCREAMING_SNAKE_CASE      =				[[0 for _ in range(size + 1						)] for _ in range(SCREAMING_SNAKE_CASE_						)]
   _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(SCREAMING_SNAKE_CASE_						):
      for col in range(SCREAMING_SNAKE_CASE_						):
         _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(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)						)[
          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    ,      SCREAMING_SNAKE_CASE_						):
         _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    ,      SCREAMING_SNAKE_CASE_						):
      for row in range(SCREAMING_SNAKE_CASE_						):
         _SCREAMING_SNAKE_CASE      =				augmented[row][col] / augmented[col][col]
         for cola in range(SCREAMING_SNAKE_CASE_    ,      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(SCREAMING_SNAKE_CASE_						)
   ]
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     Callable[[int], int]:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE      =				len(SCREAMING_SNAKE_CASE_						)
   _SCREAMING_SNAKE_CASE      =				[[0 for _ in range(SCREAMING_SNAKE_CASE_						)] for _ in range(SCREAMING_SNAKE_CASE_						)]
   _SCREAMING_SNAKE_CASE      =				[[0] for _ in range(SCREAMING_SNAKE_CASE_						)]
   _SCREAMING_SNAKE_CASE      =				42
   _SCREAMING_SNAKE_CASE      =				42
   _SCREAMING_SNAKE_CASE      =				42
   _SCREAMING_SNAKE_CASE      =				42

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

   _SCREAMING_SNAKE_CASE      =				solve(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						)

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

   return interpolated_func
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     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_	(				SCREAMING_SNAKE_CASE_ = question_function    ,      SCREAMING_SNAKE_CASE_ = 10						)     ->     int:




   """simple docstring"""
   _SCREAMING_SNAKE_CASE      =				[func(SCREAMING_SNAKE_CASE_						) 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(SCREAMING_SNAKE_CASE_						) == poly(SCREAMING_SNAKE_CASE_						):
         x_val += 1

      ret += poly(SCREAMING_SNAKE_CASE_						)

   return ret


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








'''simple docstring'''



def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     int:




   """simple docstring"""

   if not isinstance(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						):
      raise ValueError("""multiplicative_persistence() only accepts integral values"""						)
   if num < 0:
      raise ValueError("""multiplicative_persistence() does not accept negative values"""						)

   _SCREAMING_SNAKE_CASE      =				0
   _SCREAMING_SNAKE_CASE      =				str(SCREAMING_SNAKE_CASE_						)

   while len(SCREAMING_SNAKE_CASE_						) != 1:
      _SCREAMING_SNAKE_CASE      =				[int(SCREAMING_SNAKE_CASE_						) for i in num_string]

      _SCREAMING_SNAKE_CASE      =				1
      for i in range(0    ,      len(SCREAMING_SNAKE_CASE_						)						):
         total *= numbers[i]

      _SCREAMING_SNAKE_CASE      =				str(SCREAMING_SNAKE_CASE_						)

      steps += 1
   return steps
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     int:




   """simple docstring"""

   if not isinstance(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						):
      raise ValueError("""additive_persistence() only accepts integral values"""						)
   if num < 0:
      raise ValueError("""additive_persistence() does not accept negative values"""						)

   _SCREAMING_SNAKE_CASE      =				0
   _SCREAMING_SNAKE_CASE      =				str(SCREAMING_SNAKE_CASE_						)

   while len(SCREAMING_SNAKE_CASE_						) != 1:
      _SCREAMING_SNAKE_CASE      =				[int(SCREAMING_SNAKE_CASE_						) for i in num_string]

      _SCREAMING_SNAKE_CASE      =				0
      for i in range(0    ,      len(SCREAMING_SNAKE_CASE_						)						):
         total += numbers[i]

      _SCREAMING_SNAKE_CASE      =				str(SCREAMING_SNAKE_CASE_						)

      steps += 1
   return steps


if __name__ == "__main__":
     import doctest

     doctest.testmod()






