

'''simple docstring'''
from __future__ import annotations
class  _snake_case						:






			def __init__(   self       ,_snake_case			):
				UpperCAmelCase_			:	str      =   vertices
				UpperCAmelCase_			:	Optional[Any]      =   [[0] * vertices for _ in range(_snake_case			)]






			def 						UpperCamelCase__				(   self       ,_snake_case			):
				print("Vertex \t Distance from Source"			)
				for vertex in range(self.vertices			):
					print(_snake_case       ,"\t\t"       ,distances_from_source[vertex]			)






			def 						UpperCamelCase__				(   self       ,_snake_case       ,_snake_case			):
				UpperCAmelCase_			:	Tuple      =   1E7
				UpperCAmelCase_			:	int      =   0

				# Search not nearest vertex not in the shortest path tree
				for vertex in range(self.vertices			):
					if distances_from_source[vertex] < minimum and visited[vertex] is False:
						UpperCAmelCase_			:	Dict      =   distances_from_source[vertex]
						UpperCAmelCase_			:	Dict      =   vertex
				return min_index






			def 						UpperCamelCase__				(   self       ,_snake_case			):
				UpperCAmelCase_			:	Any      =   [int(1E7			)] * self.vertices  # distances from the source
				UpperCAmelCase_			:	str      =   0
				UpperCAmelCase_			:	Any      =   [False] * self.vertices

				for _ in range(self.vertices			):
					UpperCAmelCase_			:	List[str]      =   self.minimum_distance(_snake_case       ,_snake_case			)
					UpperCAmelCase_			:	Any      =   True

					# Update dist value of the adjacent vertices
					# of the picked vertex only if the current
					# distance is greater than new distance and
					# the vertex in not in the shortest path tree
					for v in range(self.vertices			):
						if (
						    self.graph[u][v] > 0
						    and visited[v] is False
						    and distances[v] > distances[u] + self.graph[u][v]
						):
							UpperCAmelCase_			:	int      =   distances[u] + self.graph[u][v]

				self.print_solution(_snake_case			)


if __name__ == "__main__":
					_lowerCamelCase	 =			Graph(9)
					_lowerCamelCase	 =			[
					    [0, 4, 0, 0, 0, 0, 0, 8, 0],
					    [4, 0, 8, 0, 0, 0, 0, 11, 0],
					    [0, 8, 0, 7, 0, 4, 0, 0, 2],
					    [0, 0, 7, 0, 9, 14, 0, 0, 0],
					    [0, 0, 0, 9, 0, 10, 0, 0, 0],
					    [0, 0, 4, 14, 10, 0, 2, 0, 0],
					    [0, 0, 0, 0, 0, 2, 0, 1, 6],
					    [8, 11, 0, 0, 0, 0, 1, 0, 7],
					    [0, 0, 2, 0, 0, 0, 6, 7, 0],
					]
					graph.dijkstra(0)







'''simple docstring'''
from __future__ import annotations


def       a__    (  _SCREAMING_SNAKE_CASE					:    int							)			-> set[int]:


	"""simple docstring"""





	UpperCAmelCase_			:	Dict      =   {1}
	UpperCAmelCase_			:	int      =   [1]
	for _ in range(2     ,							depth + 1							):
		UpperCAmelCase_			:	Dict      =   [*previous_coefficients, 0]
		UpperCAmelCase_			:	Tuple      =   [0, *previous_coefficients]
		UpperCAmelCase_			:	Dict      =   []
		for x, y in zip(_SCREAMING_SNAKE_CASE     ,							_SCREAMING_SNAKE_CASE							):
			coefficients.add(x + y							)
			previous_coefficients.append(x + y							)
	return coefficients


def       a__    (  _SCREAMING_SNAKE_CASE					:    set[int]							)			-> set[int]:


	"""simple docstring"""





	UpperCAmelCase_			:	List[Any]      =   set()
	for number in unique_coefficients:
		UpperCAmelCase_			:	Tuple      =   2
		UpperCAmelCase_			:	Tuple      =   number
		while divisor**2 <= copy_number:
			UpperCAmelCase_			:	List[Any]      =   0
			while copy_number % divisor == 0:
				copy_number //= divisor
				multiplicity += 1
			if multiplicity >= 2:
				non_squarefrees.add(_SCREAMING_SNAKE_CASE							)
				break
			divisor += 1

	return unique_coefficients.difference(_SCREAMING_SNAKE_CASE							)


def       a__    (  _SCREAMING_SNAKE_CASE					:    int = 51							)			-> int:


	"""simple docstring"""





	UpperCAmelCase_			:	Optional[Any]      =   get_pascal_triangle_unique_coefficients(_SCREAMING_SNAKE_CASE							)
	UpperCAmelCase_			:	Union[str, Any]      =   get_squarefrees(_SCREAMING_SNAKE_CASE							)
	return sum(_SCREAMING_SNAKE_CASE							)


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




