






'''simple docstring'''





from __future__ import annotations
class 				lowercase       :


				'''simple docstring'''

				def __init__(					self     :     Optional[int]				,     __lowerCamelCase     :     int     )							->							None:

					'''simple docstring'''




					lowerCamelCase__  =     order

					# a_{0} ... a_{k}
					lowerCamelCase__  =     [1.0] + [0.0] * order
					# b_{0} ... b_{k}
					lowerCamelCase__  =     [1.0] + [0.0] * order

					# x[n-1] ... x[n-k]
					lowerCamelCase__  =     [0.0] * self.order
					# y[n-1] ... y[n-k]
					lowerCamelCase__  =     [0.0] * self.order

				def    a__				(					self     :     Dict				,     __lowerCamelCase     :     list[float]				,     __lowerCamelCase     :     list[float]     )							->							None:

					'''simple docstring'''




					if len(__lowerCamelCase     ) < self.order:
						lowerCamelCase__  =     [1.0, *a_coeffs]

					if len(__lowerCamelCase     ) != self.order + 1:
						lowerCamelCase__  =     (
						    f'''Expected a_coeffs to have {self.order + 1} elements '''
						    f'''for {self.order}-order filter, got {len(__lowerCamelCase     )}'''
						)
						raise ValueError(__lowerCamelCase     )

					if len(__lowerCamelCase     ) != self.order + 1:
						lowerCamelCase__  =     (
						    f'''Expected b_coeffs to have {self.order + 1} elements '''
						    f'''for {self.order}-order filter, got {len(__lowerCamelCase     )}'''
						)
						raise ValueError(__lowerCamelCase     )

					lowerCamelCase__  =     a_coeffs
					lowerCamelCase__  =     b_coeffs




				def    a__				(					self     :     Dict				,     __lowerCamelCase     :     float     )							->							float:

					'''simple docstring'''




					lowerCamelCase__  =     0.0

					# Start at index 1 and do index 0 at the end.
					for i in range(1				,     self.order + 1     ):
						result += (
						    self.b_coeffs[i] * self.input_history[i - 1]
						    - self.a_coeffs[i] * self.output_history[i - 1]
						)

					lowerCamelCase__  =     (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

					lowerCamelCase__  =     self.input_history[:-1]
					lowerCamelCase__  =     self.output_history[:-1]

					lowerCamelCase__  =     sample
					lowerCamelCase__  =     result

					return result









'''simple docstring'''





def    lowerCamelCase_     (    lowercase__				,     lowercase__				,     lowercase__):

 def update_area_of_max_square(lowercase__				,     lowercase__) -> int:
  # BASE CASE
  if row >= rows or col >= cols:
   return 0

  lowerCamelCase__  =     update_area_of_max_square(lowercase__				,     col + 1)
  lowerCamelCase__  =     update_area_of_max_square(row + 1				,     col + 1)
  lowerCamelCase__  =     update_area_of_max_square(row + 1				,     lowercase__)

  if mat[row][col]:
   lowerCamelCase__  =     1 + min([right, diagonal, down])
   lowerCamelCase__  =     max(largest_square_area[0]				,     lowercase__)
   return sub_problem_sol
  else:
   return 0

 lowerCamelCase__  =     [0]
 update_area_of_max_square(0				,     0)
 return largest_square_area[0]






def    lowerCamelCase_     (    lowercase__				,     lowercase__				,     lowercase__):

 def update_area_of_max_square_using_dp_array(
     lowercase__				,     lowercase__				,     lowercase__) -> int:
  if row >= rows or col >= cols:
   return 0
  if dp_array[row][col] != -1:
   return dp_array[row][col]

  lowerCamelCase__  =     update_area_of_max_square_using_dp_array(lowercase__				,     col + 1				,     lowercase__)
  lowerCamelCase__  =     update_area_of_max_square_using_dp_array(row + 1				,     col + 1				,     lowercase__)
  lowerCamelCase__  =     update_area_of_max_square_using_dp_array(row + 1				,     lowercase__				,     lowercase__)

  if mat[row][col]:
   lowerCamelCase__  =     1 + min([right, diagonal, down])
   lowerCamelCase__  =     max(largest_square_area[0]				,     lowercase__)
   lowerCamelCase__  =     sub_problem_sol
   return sub_problem_sol
  else:
   return 0

 lowerCamelCase__  =     [0]
 lowerCamelCase__  =     [[-1] * cols for _ in range(lowercase__)]
 update_area_of_max_square_using_dp_array(0				,     0				,     lowercase__)

 return largest_square_area[0]






def    lowerCamelCase_     (    lowercase__				,     lowercase__				,     lowercase__):
 lowerCamelCase__  =     [[0] * (cols + 1) for _ in range(rows + 1)]
 lowerCamelCase__  =     0
 for row in range(rows - 1				,     -1				,     -1):
  for col in range(cols - 1				,     -1				,     -1):
   lowerCamelCase__  =     dp_array[row][col + 1]
   lowerCamelCase__  =     dp_array[row + 1][col + 1]
   lowerCamelCase__  =     dp_array[row + 1][col]

   if mat[row][col] == 1:
    lowerCamelCase__  =     1 + min(lowercase__				,     lowercase__				,     lowercase__)
    lowerCamelCase__  =     max(dp_array[row][col]				,     lowercase__)
   else:
    lowerCamelCase__  =     0

 return largest_square_area






def    lowerCamelCase_     (    lowercase__				,     lowercase__				,     lowercase__):
 lowerCamelCase__  =     [0] * (cols + 1)
 lowerCamelCase__  =     [0] * (cols + 1)
 lowerCamelCase__  =     0
 for row in range(rows - 1				,     -1				,     -1):
  for col in range(cols - 1				,     -1				,     -1):
   lowerCamelCase__  =     current_row[col + 1]
   lowerCamelCase__  =     next_row[col + 1]
   lowerCamelCase__  =     next_row[col]

   if mat[row][col] == 1:
    lowerCamelCase__  =     1 + min(lowercase__				,     lowercase__				,     lowercase__)
    lowerCamelCase__  =     max(current_row[col]				,     lowercase__)
   else:
    lowerCamelCase__  =     0
  lowerCamelCase__  =     current_row

 return largest_square_area


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(largest_square_area_in_matrix_bottom_up(2, 2, [[1, 1], [1, 1]]))

