






"""simple docstring"""




from __future__ import annotations






def 							lowerCAmelCase			(   UpperCamelCase_:				int  ,			UpperCamelCase_:				int  ,			UpperCamelCase_:				int       )							->				tuple[float, float]:







  '''simple docstring'''







  assert (
      c % greatest_common_divisor(UpperCamelCase_  ,			UpperCamelCase_       ) == 0
  )  # greatest_common_divisor(a,b) function implemented below
  ((_a)      ,						(_a)      ,						(_a))					      =						extended_gcd(UpperCamelCase_  ,			UpperCamelCase_       )  # extended_gcd(a,b) function implemented below
  _a					      =						c / d
  return (r * x, r * y)






def 							lowerCAmelCase			(   UpperCamelCase_:				int  ,			UpperCamelCase_:				int  ,			UpperCamelCase_:				int  ,			UpperCamelCase_:				int = 2       )							->				None:







  '''simple docstring'''







  ((_a)      ,						(_a))					      =						diophantine(UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       )  # Initial value
  _a					      =						greatest_common_divisor(UpperCamelCase_  ,			UpperCamelCase_       )
  _a					      =						a // d
  _a					      =						b // d

  for i in range(UpperCamelCase_       ):
    _a					      =						xa + i * q
    _a					      =						ya - i * p
    print(UpperCamelCase_  ,			UpperCamelCase_       )






def 							lowerCAmelCase			(   UpperCamelCase_:				int  ,			UpperCamelCase_:				int       )							->				int:







  '''simple docstring'''







  if a < b:
    _a      ,						_a					      =						b, a

  while a % b != 0:
    _a      ,						_a					      =						b, a % b

  return b






def 							lowerCAmelCase			(   UpperCamelCase_:				int  ,			UpperCamelCase_:				int       )							->				tuple[int, int, int]:







  '''simple docstring'''







  assert a >= 0 and b >= 0

  if b == 0:
    _a      ,						_a      ,						_a					      =						a, 1, 0
  else:
    ((_a)      ,						(_a)      ,						(_a))					      =						extended_gcd(UpperCamelCase_  ,			a % b       )
    _a					      =						q
    _a					      =						p - q * (a // b)

  assert a % d == 0 and b % d == 0
  assert d == a * x + b * y

  return (d, x, y)


if __name__ == "__main__":
     from doctest import testmod

     testmod(name="""diophantine""", verbose=True)
     testmod(name="""diophantine_all_soln""", verbose=True)
     testmod(name="""extended_gcd""", verbose=True)
     testmod(name="""greatest_common_divisor""", verbose=True)










"""simple docstring"""




UpperCamelCase											=     [
    [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
    [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0],
    [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0],
]






def 							lowerCAmelCase			(   UpperCamelCase_:				int  ,			UpperCamelCase_:				int  ,			UpperCamelCase_:				int  ,			UpperCamelCase_:				int       )							->				bool:







  '''simple docstring'''







  return 0 <= row < rows and 0 <= col < cols






def 							lowerCAmelCase			(   UpperCamelCase_:				int  ,			UpperCamelCase_:				int  ,			UpperCamelCase_:				set  ,			UpperCamelCase_:				list[list[int]]       )							->				int:







  '''simple docstring'''







  _a					      =						len(UpperCamelCase_       )
  _a					      =						len(mat[0]       )
  if is_safe(UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       ) and (row, col) not in seen and mat[row][col] == 1:
    seen.add((row, col)       )
    return (
        1
        + depth_first_search(row + 1  ,			UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       )
        + depth_first_search(row - 1  ,			UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       )
        + depth_first_search(UpperCamelCase_  ,			col + 1  ,			UpperCamelCase_  ,			UpperCamelCase_       )
        + depth_first_search(UpperCamelCase_  ,			col - 1  ,			UpperCamelCase_  ,			UpperCamelCase_       )
    )
  else:
    return 0






def 							lowerCAmelCase			(   UpperCamelCase_:				list[list[int]]       )							->				int:







  '''simple docstring'''







  _a					      =						set()

  _a					      =						0
  for row, line in enumerate(UpperCamelCase_       ):
    for col, item in enumerate(UpperCamelCase_       ):
      if item == 1 and (row, col) not in seen:
        # Maximizing the area
        _a					      =						max(UpperCamelCase_  ,			depth_first_search(UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       )       )
  return max_area


if __name__ == "__main__":
     import doctest

     print(find_max_area(matrix))  # Output -> 6
     doctest.testmod()


