

"""simple docstring"""






import math
import sys






class       _UpperCAmelCase     :
			def __init__(						self       )      ->      Optional[int]:






				'''simple docstring'''







				_UpperCAmelCase      :							List[Any]       =   0
				_UpperCAmelCase      :							List[Any]       =   []
				_UpperCAmelCase      :							str       =   {}  # To store the pos of node in array
			def 							__snake_case	(						self       )      ->      str:






				'''simple docstring'''







				return self.cur_size == 0
			def 							__snake_case	(						self ,						_A       )      ->      Tuple:






				'''simple docstring'''







				_UpperCAmelCase      :							Tuple       =   self.left(_A       )
				_UpperCAmelCase      :							List[str]       =   self.right(_A       )
				if lc < self.cur_size and self.array(_A       )[0] < self.array(_A       )[0]:
					_UpperCAmelCase      :							Optional[Any]       =   lc
				else:
					_UpperCAmelCase      :							Tuple       =   idx
				if rc < self.cur_size and self.array(_A       )[0] < self.array(_A       )[0]:
					_UpperCAmelCase      :							Tuple       =   rc
				if smallest != idx:
					self.swap(_A ,						_A       )
					self.min_heapify(_A       )
			def 							__snake_case	(						self ,						_A       )      ->      List[str]:






				'''simple docstring'''







				_UpperCAmelCase      :							Optional[int]       =   self.cur_size
				self.cur_size += 1
				self.array.append((sys.maxsize, tup[1])       )
				self.decrease_key((sys.maxsize, tup[1]) ,						tup[0]       )
			def 							__snake_case	(						self       )      ->      Dict:






				'''simple docstring'''







				_UpperCAmelCase      :							List[str]       =   self.array[0][1]
				_UpperCAmelCase      :							Tuple       =   self.array[self.cur_size - 1]
				self.cur_size -= 1
				self.min_heapify(1       )
				del self.pos[min_node]
				return min_node
			def 							__snake_case	(						self ,						_A       )      ->      Union[str, Any]:






				'''simple docstring'''







				return 2 * i + 1
			def 							__snake_case	(						self ,						_A       )      ->      List[Any]:






				'''simple docstring'''







				return 2 * i + 2
			def 							__snake_case	(						self ,						_A       )      ->      List[Any]:






				'''simple docstring'''







				return math.floor(i / 2       )
			def 							__snake_case	(						self ,						_A ,						_A       )      ->      Dict:






				'''simple docstring'''







				_UpperCAmelCase      :							List[str]       =   j
				_UpperCAmelCase      :							Dict       =   i
				_UpperCAmelCase      :							Union[str, Any]       =   self.array[i]
				_UpperCAmelCase      :							Union[str, Any]       =   self.array[j]
				_UpperCAmelCase      :							str       =   temp
			def 							__snake_case	(						self ,						_A ,						_A       )      ->      Any:






				'''simple docstring'''







				_UpperCAmelCase      :							Union[str, Any]       =   self.pos[tup[1]]
				# assuming the new_d is atmost old_d
				_UpperCAmelCase      :							Any       =   (new_d, tup[1])
				while idx > 0 and self.array[self.par(_A       )][0] > self.array[idx][0]:
					self.swap(_A ,						self.par(_A       )       )
					_UpperCAmelCase      :							Optional[int]       =   self.par(_A       )






class       _UpperCAmelCase     :
			def __init__(						self ,						_A       )      ->      str:






				'''simple docstring'''







				_UpperCAmelCase      :							Tuple       =   {}  # To store graph: u -> (v,w)
				_UpperCAmelCase      :							Tuple       =   num  # Number of nodes in graph
				# To store the distance from source vertex
				_UpperCAmelCase      :							Any       =   [0] * self.num_nodes
				_UpperCAmelCase      :							Optional[int]       =   [-1] * self.num_nodes  # To store the path
			def 							__snake_case	(						self ,						_A ,						_A ,						_A       )      ->      Dict:






				'''simple docstring'''







				if u in self.adjList:
					self.adjList[u].append((v, w)       )
				else:
					_UpperCAmelCase      :							str       =   [(v, w)]

				# Assuming undirected graph
				if v in self.adjList:
					self.adjList[v].append((u, w)       )
				else:
					_UpperCAmelCase      :							Any       =   [(u, w)]
			def 							__snake_case	(						self       )      ->      Dict:






				'''simple docstring'''







				for u in self.adjList:
					print(_A ,						"""->""" ,						""" -> """.join(str(f'''{v}({w})'''       ) for v, w in self.adjList[u]       )       )
			def 							__snake_case	(						self ,						_A       )      ->      List[Any]:






				'''simple docstring'''







				_UpperCAmelCase      :							int       =   [-1] * self.num_nodes
				# src is the source node
				_UpperCAmelCase      :							str       =   0
				_UpperCAmelCase      :							str       =   PriorityQueue()
				q.insert((0, src)       )  # (dist from src, node)
				for u in self.adjList:
					if u != src:
						_UpperCAmelCase      :							Dict       =   sys.maxsize  # Infinity
						_UpperCAmelCase      :							Optional[Any]       =   -1

				while not q.is_empty():
					_UpperCAmelCase      :							List[str]       =   q.extract_min()  # Returns node with the min dist from source
					# Update the distance of all the neighbours of u and
					# if their prev dist was INFINITY then push them in Q
					for v, w in self.adjList[u]:
						_UpperCAmelCase      :							Dict       =   self.dist[u] + w
						if self.dist[v] > new_dist:
							if self.dist[v] == sys.maxsize:
								q.insert((new_dist, v)       )
							else:
								q.decrease_key((self.dist[v], v) ,						_A       )
							_UpperCAmelCase      :							Dict       =   new_dist
							_UpperCAmelCase      :							str       =   u

        # Show the shortest distances from src
				self.show_distances(_A       )
			def 							__snake_case	(						self ,						_A       )      ->      Any:






				'''simple docstring'''







				print(f'''Distance from node: {src}'''       )
				for u in range(self.num_nodes       ):
					print(f'''Node {u} has distance: {self.dist[u]}'''       )
			def 							__snake_case	(						self ,						_A ,						_A       )      ->      Dict:






				'''simple docstring'''







				_UpperCAmelCase      :							List[str]       =   []
				_UpperCAmelCase      :							List[Any]       =   0
				_UpperCAmelCase      :							Dict       =   dest
				# Backtracking from dest to src
				while self.par[temp] != -1:
					path.append(_A       )
					if temp != src:
						for v, w in self.adjList[temp]:
							if v == self.par[temp]:
								cost += w
								break
					_UpperCAmelCase      :							Tuple       =   self.par[temp]
				path.append(_A       )
				path.reverse()

				print(f'''----Path to reach {dest} from {src}----'''       )
				for u in path:
					print(f'''{u}''' ,						end=""" """       )
					if u != dest:
						print("""-> """ ,						end=""""""       )

				print("""\nTotal cost of path: """ ,						_A       )


if __name__ == "__main__":
						lowerCamelCase__			:					List[Any]							  =					Graph(9)
						graph.add_edge(0, 1, 4)
						graph.add_edge(0, 7, 8)
						graph.add_edge(1, 2, 8)
						graph.add_edge(1, 7, 11)
						graph.add_edge(2, 3, 7)
						graph.add_edge(2, 8, 2)
						graph.add_edge(2, 5, 4)
						graph.add_edge(3, 4, 9)
						graph.add_edge(3, 5, 14)
						graph.add_edge(4, 5, 10)
						graph.add_edge(5, 6, 2)
						graph.add_edge(6, 7, 1)
						graph.add_edge(6, 8, 6)
						graph.add_edge(7, 8, 7)
						graph.show_graph()
						graph.dijkstra(0)
						graph.show_path(0, 4)

# OUTPUT
# 0 -> 1(4) -> 7(8)
# 1 -> 0(4) -> 2(8) -> 7(11)
# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7)
# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4)
# 3 -> 2(7) -> 4(9) -> 5(14)
# 8 -> 2(2) -> 6(6) -> 7(7)
# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2)
# 4 -> 3(9) -> 5(10)
# 6 -> 5(2) -> 7(1) -> 8(6)
# Distance from node: 0
# Node 0 has distance: 0
# Node 1 has distance: 4
# Node 2 has distance: 12
# Node 3 has distance: 19
# Node 4 has distance: 21
# Node 5 has distance: 11
# Node 6 has distance: 9
# Node 7 has distance: 8
# Node 8 has distance: 14
# ----Path to reach 4 from 0----
# 0 -> 7 -> 6 -> 5 -> 4
# Total cost of path:  21








"""simple docstring"""






from math import factorial
def  UpperCamelCase   (     _lowerCAmelCase       :  Dict,					_lowerCAmelCase       :  List[str]	)			->     Dict:
	return factorial(_lowerCAmelCase	) / (factorial(_lowerCAmelCase	) * factorial(n - r	))
def  UpperCamelCase   (     )			->     Tuple:
	_UpperCAmelCase      :							Optional[int]       =   0

	for i in range(1,					101	):
		for j in range(1,					i + 1	):
			if combinations(_lowerCAmelCase,					_lowerCAmelCase	) > 1E6:
				total += 1
	return total


if __name__ == "__main__":
						print(solution())





