'''simple docstring'''

import os
import socket
from contextlib import contextmanager

import torch

from ..commands.config.default import write_basic_config  # noqa: F401
from ..state import PartialState
from .dataclasses import DistributedType
from .imports import is_deepspeed_available, is_tpu_available
from .transformer_engine import convert_model
from .versions import is_torch_version


if is_deepspeed_available():
  from deepspeed import DeepSpeedEngine

if is_tpu_available(check_device=False):
  import torch_xla.core.xla_model as xm
def 			__UpperCamelCase       (   UpperCAmelCase     ):
 if is_torch_version('''<'''		,     '''2.0.0'''     ) or not hasattr(UpperCAmelCase		,     '''_dynamo'''     ):
  return False
 return isinstance(UpperCAmelCase		,     torch._dynamo.eval_frame.OptimizedModule     )
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase = True     ):
 lowercase__				:    Dict  =					(torch.nn.parallel.DistributedDataParallel, torch.nn.DataParallel)

 lowercase__				:    List[str]  =					is_compiled_module(UpperCAmelCase     )
 if is_compiled:
  lowercase__				:    List[Any]  =					model
  lowercase__				:    Optional[int]  =					model._orig_mod

 if is_deepspeed_available():
  options += (DeepSpeedEngine,)

 while isinstance(UpperCAmelCase		,     UpperCAmelCase     ):
  lowercase__				:    str  =					model.module

 if not keep_fpaa_wrapper:
  lowercase__				:    List[Any]  =					getattr(UpperCAmelCase		,     '''forward'''     )
  lowercase__				:    Tuple  =					model.__dict__.pop('''_original_forward'''		,     UpperCAmelCase     )
  if original_forward is not None:
   while hasattr(UpperCAmelCase		,     '''__wrapped__'''     ):
    lowercase__				:    Optional[Any]  =					forward.__wrapped__
    if forward == original_forward:
     break
   lowercase__				:    Union[str, Any]  =					forward
  if getattr(UpperCAmelCase		,     '''_converted_to_transformer_engine'''		,     UpperCAmelCase     ):
   convert_model(UpperCAmelCase		,     to_transformer_engine=UpperCAmelCase     )

 if is_compiled:
  lowercase__				:    Optional[Any]  =					model
  lowercase__				:    Optional[Any]  =					compiled_model

 return model
def 			__UpperCamelCase       (   ):
 PartialState().wait_for_everyone()
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
 if PartialState().distributed_type == DistributedType.TPU:
  xm.save(UpperCAmelCase		,     UpperCAmelCase     )
 elif PartialState().local_process_index == 0:
  torch.save(UpperCAmelCase		,     UpperCAmelCase     )
@contextmanager
def 			__UpperCamelCase       (   **UpperCAmelCase     ):
 for key, value in kwargs.items():
  lowercase__				:    Dict  =					str(UpperCAmelCase     )

 yield

 for key in kwargs:
  if key.upper() in os.environ:
   del os.environ[key.upper()]
def 			__UpperCamelCase       (   UpperCAmelCase     ):
 if not hasattr(UpperCAmelCase		,     '''__qualname__'''     ) and not hasattr(UpperCAmelCase		,     '''__name__'''     ):
  lowercase__				:    Any  =					getattr(UpperCAmelCase		,     '''__class__'''		,     UpperCAmelCase     )
 if hasattr(UpperCAmelCase		,     '''__qualname__'''     ):
  return obj.__qualname__
 if hasattr(UpperCAmelCase		,     '''__name__'''     ):
  return obj.__name__
 return str(UpperCAmelCase     )
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
 for key, value in source.items():
  if isinstance(UpperCAmelCase		,     UpperCAmelCase     ):
   lowercase__				:    str  =					destination.setdefault(UpperCAmelCase		,     {}     )
   merge_dicts(UpperCAmelCase		,     UpperCAmelCase     )
  else:
   lowercase__				:    Optional[Any]  =					value

 return destination





def 			__UpperCamelCase       (   UpperCAmelCase = None     ):
 if port is None:
  lowercase__				:    int  =					2_9500
 with socket.socket(socket.AF_INET		,     socket.SOCK_STREAM     ) as s:
  return s.connect_ex(('''localhost''', port)     ) == 0


'''simple docstring'''

def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     ):

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

  lowercase__				:    int  =					update_area_of_max_square(UpperCAmelCase		,     col + 1     )
  lowercase__				:    Any  =					update_area_of_max_square(row + 1		,     col + 1     )
  lowercase__				:    str  =					update_area_of_max_square(row + 1		,     UpperCAmelCase     )

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

 lowercase__				:    Dict  =					[0]
 update_area_of_max_square(0		,     0     )
 return largest_square_area[0]
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     ):

 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]

  lowercase__				:    int  =					update_area_of_max_square_using_dp_array(UpperCAmelCase		,     col + 1		,     UpperCAmelCase     )
  lowercase__				:    Optional[int]  =					update_area_of_max_square_using_dp_array(row + 1		,     col + 1		,     UpperCAmelCase     )
  lowercase__				:    Any  =					update_area_of_max_square_using_dp_array(row + 1		,     UpperCAmelCase		,     UpperCAmelCase     )

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

 lowercase__				:    Any  =					[0]
 lowercase__				:    List[Any]  =					[[-1] * cols for _ in range(UpperCAmelCase     )]
 update_area_of_max_square_using_dp_array(0		,     0		,     UpperCAmelCase     )

 return largest_square_area[0]
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     ):
 lowercase__				:    Optional[int]  =					[[0] * (cols + 1) for _ in range(rows + 1     )]
 lowercase__				:    str  =					0
 for row in range(rows - 1		,     -1		,     -1     ):
  for col in range(cols - 1		,     -1		,     -1     ):
   lowercase__				:    str  =					dp_array[row][col + 1]
   lowercase__				:    Optional[Any]  =					dp_array[row + 1][col + 1]
   lowercase__				:    str  =					dp_array[row + 1][col]

   if mat[row][col] == 1:
    lowercase__				:    Dict  =					1 + min(UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     )
    lowercase__				:    str  =					max(dp_array[row][col]		,     UpperCAmelCase     )
   else:
    lowercase__				:    Any  =					0

 return largest_square_area
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     ):
 lowercase__				:    List[str]  =					[0] * (cols + 1)
 lowercase__				:    str  =					[0] * (cols + 1)
 lowercase__				:    Tuple  =					0
 for row in range(rows - 1		,     -1		,     -1     ):
  for col in range(cols - 1		,     -1		,     -1     ):
   lowercase__				:    List[Any]  =					current_row[col + 1]
   lowercase__				:    Any  =					next_row[col + 1]
   lowercase__				:    Optional[Any]  =					next_row[col]

   if mat[row][col] == 1:
    lowercase__				:    List[str]  =					1 + min(UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase     )
    lowercase__				:    List[str]  =					max(current_row[col]		,     UpperCAmelCase     )
   else:
    lowercase__				:    int  =					0
  lowercase__				:    int  =					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]]))

