

from __future__ import annotations

from collections.abc import Callable

__A			:					Optional[Any]						=			list[list[float | int]]





def 	__a     (      A__			:  Matrix			,  A__			:  Matrix       ):
    SCREAMING_SNAKE_CASE										=   len(A__       )
    SCREAMING_SNAKE_CASE										=   [[0 for _ in range(size + 1       )] for _ in range(A__       )]
    SCREAMING_SNAKE_CASE										=   42
    SCREAMING_SNAKE_CASE										=   42
    SCREAMING_SNAKE_CASE										=   42
    SCREAMING_SNAKE_CASE										=   42
    SCREAMING_SNAKE_CASE										=   42
    SCREAMING_SNAKE_CASE										=   42

    for row in range(A__       ):
        for col in range(A__       ):
            SCREAMING_SNAKE_CASE										=   matrix[row][col]

        SCREAMING_SNAKE_CASE										=   vector[row][0]

    SCREAMING_SNAKE_CASE										=   0
    SCREAMING_SNAKE_CASE										=   0
    while row < size and col < size:
        # pivoting
        SCREAMING_SNAKE_CASE										=   max((abs(augmented[rowa][col]       ), rowa) for rowa in range(A__			,  A__       )       )[
            1
        ]
        if augmented[pivot_row][col] == 0:
            col += 1
            continue
        else:
            SCREAMING_SNAKE_CASE							,	SCREAMING_SNAKE_CASE										=   augmented[pivot_row], augmented[row]

        for rowa in range(row + 1			,  A__       ):
            SCREAMING_SNAKE_CASE										=   augmented[rowa][col] / augmented[row][col]
            SCREAMING_SNAKE_CASE										=   0
            for cola in range(col + 1			,  size + 1       ):
                augmented[rowa][cola] -= augmented[row][cola] * ratio

        row += 1
        col += 1

    # back substitution
    for col in range(1			,  A__       ):
        for row in range(A__       ):
            SCREAMING_SNAKE_CASE										=   augmented[row][col] / augmented[col][col]
            for cola in range(A__			,  size + 1       ):
                augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
    return [
        [round(augmented[row][size] / augmented[row][row]			,  10       )] for row in range(A__       )
    ]





def 	__a     (      A__			:  list[int]       ):
    SCREAMING_SNAKE_CASE										=   len(A__       )
    SCREAMING_SNAKE_CASE										=   [[0 for _ in range(A__       )] for _ in range(A__       )]
    SCREAMING_SNAKE_CASE										=   [[0] for _ in range(A__       )]
    SCREAMING_SNAKE_CASE										=   42
    SCREAMING_SNAKE_CASE										=   42
    SCREAMING_SNAKE_CASE										=   42
    SCREAMING_SNAKE_CASE										=   42

    for x_val, y_val in enumerate(A__       ):
        for col in range(A__       ):
            SCREAMING_SNAKE_CASE										=   (x_val + 1) ** (size - col - 1)
        SCREAMING_SNAKE_CASE										=   y_val

    SCREAMING_SNAKE_CASE										=   solve(A__			,  A__       )

    def interpolated_func(A__			:  int       ) -> int:
        return sum(
            round(coeffs[x_val][0]       ) * (var ** (size - x_val - 1))
            for x_val in range(A__       )       )

    return interpolated_func





def 	__a     (      A__			:  int       ):
    return (
        1
        - variable
        + variable**2
        - variable**3
        + variable**4
        - variable**5
        + variable**6
        - variable**7
        + variable**8
        - variable**9
        + variable**10
    )





def 	__a     (      A__			:  Callable[[int], int] = question_function			,  A__			:  int = 10       ):
    SCREAMING_SNAKE_CASE										=   [func(A__       ) for x_val in range(1			,  order + 1       )]

    SCREAMING_SNAKE_CASE										=   [
        interpolate(data_points[:max_coeff]       ) for max_coeff in range(1			,  order + 1       )
    ]

    SCREAMING_SNAKE_CASE										=   0
    SCREAMING_SNAKE_CASE										=   42
    SCREAMING_SNAKE_CASE										=   42

    for poly in polynomials:
        SCREAMING_SNAKE_CASE										=   1
        while func(A__       ) == poly(A__       ):
            x_val += 1

        ret += poly(A__       )

    return ret


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


from __future__ import annotations

__A			:					str						=			list[tuple[int, int]]

__A			:					Optional[int]						=			[
    [0, 0, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 1, 0, 0, 0, 0],
    [1, 0, 1, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 1, 0, 0],
]

__A			:					List[str]						=			([-1, 0], [0, -1], [1, 0], [0, 1])  # up, left, down, right





class 			_SCREAMING_SNAKE_CASE :







   '''simple docstring'''




   def __init__(       self					:			str     , __lowerCamelCase					:			int     , __lowerCamelCase					:			int     , __lowerCamelCase					:			int     , __lowerCamelCase					:			int     , __lowerCamelCase					:			float     , __lowerCamelCase					:			Node | None     , ):
       SCREAMING_SNAKE_CASE										=   pos_x
       SCREAMING_SNAKE_CASE										=   pos_y
       SCREAMING_SNAKE_CASE										=   (pos_y, pos_x)
       SCREAMING_SNAKE_CASE										=   goal_x
       SCREAMING_SNAKE_CASE										=   goal_y
       SCREAMING_SNAKE_CASE										=   g_cost
       SCREAMING_SNAKE_CASE										=   parent
       SCREAMING_SNAKE_CASE										=   self.calculate_heuristic()





   def      _snake_case		(       self					:			Union[str, Any]			):
       SCREAMING_SNAKE_CASE										=   abs(self.pos_x - self.goal_x			)
       SCREAMING_SNAKE_CASE										=   abs(self.pos_y - self.goal_y			)
       return dx + dy





   def __lt__(       self					:			Union[str, Any]     , __lowerCamelCase					:			List[Any]			):
       return self.f_cost < other.f_cost





class 			_SCREAMING_SNAKE_CASE :







   '''simple docstring'''




   def __init__(       self					:			Optional[int]     , __lowerCamelCase					:			tuple[int, int]     , __lowerCamelCase					:			tuple[int, int]			):
       SCREAMING_SNAKE_CASE										=   Node(start[1]     , start[0]     , goal[1]     , goal[0]     , 0     , __lowerCamelCase			)
       SCREAMING_SNAKE_CASE										=   Node(goal[1]     , goal[0]     , goal[1]     , goal[0]     , 99999     , __lowerCamelCase			)

       SCREAMING_SNAKE_CASE										=   [self.start]
       SCREAMING_SNAKE_CASE										=   []

       SCREAMING_SNAKE_CASE										=   False





   def      _snake_case		(       self					:			Optional[Any]			):
       while self.open_nodes:
           # Open Nodes are sorted using __lt__
           self.open_nodes.sort()
           SCREAMING_SNAKE_CASE										=   self.open_nodes.pop(0			)

           if current_node.pos == self.target.pos:
               SCREAMING_SNAKE_CASE										=   True
               return self.retrace_path(__lowerCamelCase			)

           self.closed_nodes.append(__lowerCamelCase			)
           SCREAMING_SNAKE_CASE										=   self.get_successors(__lowerCamelCase			)

           for child_node in successors:
               if child_node in self.closed_nodes:
                   continue

               if child_node not in self.open_nodes:
                   self.open_nodes.append(__lowerCamelCase			)
               else:
                   # retrieve the best current path
                   SCREAMING_SNAKE_CASE										=   self.open_nodes.pop(self.open_nodes.index(__lowerCamelCase			)			)

                   if child_node.g_cost < better_node.g_cost:
                       self.open_nodes.append(__lowerCamelCase			)
                   else:
                       self.open_nodes.append(__lowerCamelCase			)

       if not self.reached:
           return [self.start.pos]
       return None





   def      _snake_case		(       self					:			List[Any]     , __lowerCamelCase					:			Node			):
       SCREAMING_SNAKE_CASE										=   []
       for action in delta:
           SCREAMING_SNAKE_CASE										=   parent.pos_x + action[1]
           SCREAMING_SNAKE_CASE										=   parent.pos_y + action[0]

           if not (0 <= pos_x <= len(grid[0]			) - 1 and 0 <= pos_y <= len(__lowerCamelCase			) - 1):
               continue

           if grid[pos_y][pos_x] != 0:
               continue

           successors.append(
               Node(
                   __lowerCamelCase     , __lowerCamelCase     , self.target.pos_y     , self.target.pos_x     , parent.g_cost + 1     , __lowerCamelCase     , )			)
       return successors





   def      _snake_case		(       self					:			str     , __lowerCamelCase					:			Node | None			):
       SCREAMING_SNAKE_CASE										=   node
       SCREAMING_SNAKE_CASE										=   []
       while current_node is not None:
           path.append((current_node.pos_y, current_node.pos_x)			)
           SCREAMING_SNAKE_CASE										=   current_node.parent
       path.reverse()
       return path


if __name__ == "__main__":
    __A			:					Optional[Any]						=			(0, 0)
    __A			:					Optional[int]						=			(len(grid) - 1, len(grid[0]) - 1)
    for elem in grid:
        print(elem)

    print('------')

    __A			:					List[str]						=			GreedyBestFirst(init, goal)
    __A			:					Tuple						=			greedy_bf.search()
    if path:
        for pos_x, pos_y in path:
            __A			:					Optional[Any]						=			2

        for elem in grid:
            print(elem)