
from numpy import exp, pi, sqrt






def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_ = 0.0	,	UpperCamelCase_ = 1.0		)		->		int:
					'''simple docstring'''


					return 1 / sqrt(2 * pi * sigma**2		) * exp(-((x - mu) ** 2) / (2 * sigma**2)		)


if __name__ == "__main__":
				import doctest

				doctest.testmod()







def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)		->		int:
					'''simple docstring'''


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

										SCREAMING_SNAKE_CASE__													= update_area_of_max_square(UpperCamelCase_	,	col + 1		)
										SCREAMING_SNAKE_CASE__													= update_area_of_max_square(row + 1	,	col + 1		)
										SCREAMING_SNAKE_CASE__													= update_area_of_max_square(row + 1	,	UpperCamelCase_		)

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

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






def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)		->		int:
					'''simple docstring'''


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

										SCREAMING_SNAKE_CASE__													= update_area_of_max_square_using_dp_array(UpperCamelCase_	,	col + 1	,	UpperCamelCase_		)
										SCREAMING_SNAKE_CASE__													= update_area_of_max_square_using_dp_array(row + 1	,	col + 1	,	UpperCamelCase_		)
										SCREAMING_SNAKE_CASE__													= update_area_of_max_square_using_dp_array(row + 1	,	UpperCamelCase_	,	UpperCamelCase_		)

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

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

					return largest_square_area[0]






def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)		->		int:
					'''simple docstring'''


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

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

					return largest_square_area






def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)		->		int:
					'''simple docstring'''


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

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





