





'''simple docstring'''

lowercase__						:      List[Any]	=    [
    [0, 16, 13, 0, 0, 0],
    [0, 0, 10, 12, 0, 0],
    [0, 4, 0, 0, 14, 0],
    [0, 0, 9, 0, 0, 20],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]







def  a__    (    lowercase :					Tuple, lowercase :					Optional[int], lowercase :					List[Any], lowercase :					Union[str, Any]				)		->		int:





     """simple docstring"""

     _UpperCamelCase       =	[False] * len(lowercase				)
     _UpperCamelCase       =	[s]
     _UpperCamelCase       =	True

     while queue:
          _UpperCamelCase       =	queue.pop(0				)
          for ind in range(len(graph[u]				)				):
               if visited[ind] is False and graph[u][ind] > 0:
                    queue.append(lowercase				)
                    _UpperCamelCase       =	True
                    _UpperCamelCase       =	u

     return visited[t]







def  a__    (    lowercase :					Optional[Any], lowercase :					Tuple, lowercase :					Any				)		->		str:





     """simple docstring"""

     _UpperCamelCase       =	[-1] * (len(lowercase				))
     _UpperCamelCase       =	0
     _UpperCamelCase       =	[]
     _UpperCamelCase       =	[i[:] for i in graph]  # Record original cut, copy.
     while bfs(lowercase, lowercase, lowercase, lowercase				):
          _UpperCamelCase       =	float('''Inf'''				)
          _UpperCamelCase       =	sink

          while s != source:
               # Find the minimum value in select path
               _UpperCamelCase       =	min(lowercase, graph[parent[s]][s]				)
               _UpperCamelCase       =	parent[s]

          max_flow += path_flow
          _UpperCamelCase       =	sink

          while v != source:
               _UpperCamelCase       =	parent[v]
               graph[u][v] -= path_flow
               graph[v][u] += path_flow
               _UpperCamelCase       =	parent[v]

     for i in range(len(lowercase				)				):
          for j in range(len(graph[0]				)				):
               if graph[i][j] == 0 and temp[i][j] > 0:
                    res.append((i, j)				)

     return res


if __name__ == "__main__":
   print(mincut(test_graph, source=0, sink=5))










'''simple docstring'''

def  a__    (    lowercase :					int, lowercase :					int, lowercase :					list[list[int]]				)		->		int:





     """simple docstring"""

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

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

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

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







def  a__    (    lowercase :					int, lowercase :					int, lowercase :					list[list[int]]				)		->		int:





     """simple docstring"""

     def update_area_of_max_square_using_dp_array(
         lowercase :					int, lowercase :					int, lowercase :					list[list[int]]				) -> 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(lowercase, col + 1, lowercase				)
          _UpperCamelCase       =	update_area_of_max_square_using_dp_array(row + 1, col + 1, lowercase				)
          _UpperCamelCase       =	update_area_of_max_square_using_dp_array(row + 1, lowercase, lowercase				)

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

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

     return largest_square_area[0]







def  a__    (    lowercase :					int, lowercase :					int, lowercase :					list[list[int]]				)		->		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(lowercase, lowercase, lowercase				)
                    _UpperCamelCase       =	max(dp_array[row][col], lowercase				)
               else:
                    _UpperCamelCase       =	0

     return largest_square_area







def  a__    (    lowercase :					int, lowercase :					int, lowercase :					list[list[int]]				)		->		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(lowercase, lowercase, lowercase				)
                    _UpperCamelCase       =	max(current_row[col], lowercase				)
               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]]))



