



from __future__ import annotations

lowercase_						=       [
    [-1, 0],  # left
    [0, -1],  # down
    [1, 0],  # right
    [0, 1],  # up
]



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_  ,					):
			lowercase__   					=			[
			    [0 for col in range(len(grid[0]					)					)] for row in range(len(SCREAMING_SNAKE_CASE_					)					)
			]  # the reference grid
			lowercase__   					=			1
			lowercase__   					=			[
			    [0 for col in range(len(grid[0]					)					)] for row in range(len(SCREAMING_SNAKE_CASE_					)					)
			]  # the action grid

			lowercase__   					=			init[0]
			lowercase__   					=			init[1]
			lowercase__   					=			0
			lowercase__   					=			g + heuristic[x][y]  # cost from starting cell to destination cell
			lowercase__   					=			[[f, g, x, y]]

			lowercase__   					=			False  # flag that is set when search is complete
			lowercase__   					=			False  # flag set if we can't find expand

			while not found and not resign:
						if len(SCREAMING_SNAKE_CASE_					) == 0:
									raise ValueError("Algorithm is unable to find solution"					)
						else:  # to choose the least costliest action so as to move closer to the goal
									cell.sort()
									cell.reverse()
									lowercase__   					=			cell.pop()
									lowercase__   					=			next_cell[2]
									lowercase__   					=			next_cell[3]
									lowercase__   					=			next_cell[1]

									if x == goal[0] and y == goal[1]:
												lowercase__   					=			True
									else:
												for i in range(len(SCREAMING_SNAKE_CASE_					)					):  # to try out different valid actions
															lowercase__   					=			x + DIRECTIONS[i][0]
															lowercase__   					=			y + DIRECTIONS[i][1]
															if xa >= 0 and xa < len(SCREAMING_SNAKE_CASE_					) and ya >= 0 and ya < len(grid[0]					):
																		if closed[xa][ya] == 0 and grid[xa][ya] == 0:
																					lowercase__   					=			g + cost
																					lowercase__   					=			ga + heuristic[xa][ya]
																					cell.append([fa, ga, xa, ya]					)
																					lowercase__   					=			1
																					lowercase__   					=			i
			lowercase__   					=			[]
			lowercase__   					=			goal[0]
			lowercase__   					=			goal[1]
			invpath.append([x, y]					)  # we get the reverse path from here
			while x != init[0] or y != init[1]:
						lowercase__   					=			x - DIRECTIONS[action[x][y]][0]
						lowercase__   					=			y - DIRECTIONS[action[x][y]][1]
						lowercase__   					=			xa
						lowercase__   					=			ya
						invpath.append([x, y]					)

			lowercase__   					=			[]
			for i in range(len(SCREAMING_SNAKE_CASE_					)					):
						path.append(invpath[len(SCREAMING_SNAKE_CASE_					) - 1 - i]					)
			return path, action


if __name__ == "__main__":
							lowercase_						=       [
							    [0, 1, 0, 0, 0, 0],
							    [0, 1, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
							    [0, 1, 0, 0, 0, 0],
							    [0, 1, 0, 0, 1, 0],
							    [0, 0, 0, 0, 1, 0],
							]

							lowercase_						=       [0, 0]
							# all coordinates are given in format [y,x]
							lowercase_						=       [len(grid) - 1, len(grid[0]) - 1]
							lowercase_						=       1

							# the cost map which pushes the path closer to the goal
							lowercase_						=       [[0 for row in range(len(grid[0]))] for col in range(len(grid))]
							for i in range(len(grid)):
														for j in range(len(grid[0])):
																					lowercase_						=       abs(i - goal[0]) + abs(j - goal[1])
																					if grid[i][j] == 1:
																												# added extra penalty in the heuristic map
																												lowercase_						=       99

							lowercase_			,      lowercase_						=       search(grid, init, goal, cost, heuristic)

							print("""ACTION MAP""")
							for i in range(len(action)):
														print(action[i])

							for i in range(len(path)):
														print(path[i])









def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_  ,					SCREAMING_SNAKE_CASE_					):
			lowercase__   					=			1  # To kept the Calculated Value
			# Since C(n, k) = C(n, n-k)
			if k > (n - k):
						lowercase__   					=			n - k
			# Calculate C(n,k)
			for i in range(SCREAMING_SNAKE_CASE_					):
						result *= n - i
						result //= i + 1
			return result



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			return binomial_coefficient(2 * node_count  ,					SCREAMING_SNAKE_CASE_					) // (node_count + 1)



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			if n < 0:
						raise ValueError("factorial() not defined for negative values"					)
			lowercase__   					=			1
			for i in range(1  ,					n + 1					):
						result *= i
			return result



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			return catalan_number(SCREAMING_SNAKE_CASE_					) * factorial(SCREAMING_SNAKE_CASE_					)


if __name__ == "__main__":
							lowercase_						=       int(input("""Enter the number of nodes: """).strip() or 0)
							if node_count <= 0:
														raise ValueError("""We need some nodes to work with.""")
							print(
							    F'Given {node_count} nodes, there are {binary_tree_count(node_count)} '
							    F'binary trees and {catalan_number(node_count)} binary search trees.'
							)




