
"""simple docstring"""





def  lowerCamelCase__						(     __snake_case,	__snake_case,	__snake_case      )				->						int:


					"""simple docstring"""





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

										_UpperCamelCase									=    update_area_of_max_square(__snake_case,	col + 1      )
										_UpperCamelCase									=    update_area_of_max_square(row + 1,	col + 1      )
										_UpperCamelCase									=    update_area_of_max_square(row + 1,	__snake_case      )

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

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



def  lowerCamelCase__						(     __snake_case,	__snake_case,	__snake_case      )				->						int:


					"""simple docstring"""





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

										_UpperCamelCase									=    update_area_of_max_square_using_dp_array(__snake_case,	col + 1,	__snake_case      )
										_UpperCamelCase									=    update_area_of_max_square_using_dp_array(row + 1,	col + 1,	__snake_case      )
										_UpperCamelCase									=    update_area_of_max_square_using_dp_array(row + 1,	__snake_case,	__snake_case      )

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

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

					return largest_square_area[0]



def  lowerCamelCase__						(     __snake_case,	__snake_case,	__snake_case      )				->						int:


					"""simple docstring"""





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

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

					return largest_square_area



def  lowerCamelCase__						(     __snake_case,	__snake_case,	__snake_case      )				->						int:


					"""simple docstring"""





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

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








"""simple docstring"""





from __future__ import annotations

from functools import lru_cache
from math import ceil

_a								=						100

_a								=						set(range(3, NUM_PRIMES, 2))
primes.add(2)
_a								=						42

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
				if prime not in primes:
								continue
				primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))



@lru_cache(maxsize=1_00      )
def  lowerCamelCase__						(     __snake_case      )				->						set[int]:


					"""simple docstring"""





					if number_to_partition < 0:
										return set()
					elif number_to_partition == 0:
										return {1}

					_UpperCamelCase									=    set()
					_UpperCamelCase									=    42
					_UpperCamelCase									=    42

					for prime in primes:
										if prime > number_to_partition:
															continue
										for sub in partition(number_to_partition - prime      ):
															ret.add(sub * prime      )

					return ret



def  lowerCamelCase__						(     __snake_case = 50_00      )				->						int | None:


					"""simple docstring"""





					for number_to_partition in range(1,	__snake_case      ):
										if len(partition(__snake_case      )      ) > number_unique_partitions:
															return number_to_partition
					return None


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






