




import math
import sys







class __snake_case     :







   def __init__( self						:		Optional[int]):

        """simple docstring"""


        UpperCAmelCase_		=				0
        UpperCAmelCase_		=				[]
        UpperCAmelCase_		=				{}  # To store the pos of node in array







   def lowerCamelCase		( self						:		str):

        """simple docstring"""


        return self.cur_size == 0







   def lowerCamelCase		( self						:		List[str]   ,		_snake_case						:		Any):

        """simple docstring"""


        UpperCAmelCase_		=				self.left(_snake_case)
        UpperCAmelCase_		=				self.right(_snake_case)
        if lc < self.cur_size and self.array(_snake_case)[0] < self.array(_snake_case)[0]:
             UpperCAmelCase_		=				lc
        else:
             UpperCAmelCase_		=				idx
        if rc < self.cur_size and self.array(_snake_case)[0] < self.array(_snake_case)[0]:
             UpperCAmelCase_		=				rc
        if smallest != idx:
             self.swap(_snake_case   ,		_snake_case)
             self.min_heapify(_snake_case)







   def lowerCamelCase		( self						:		Union[str, Any]   ,		_snake_case						:		str):

        """simple docstring"""


        UpperCAmelCase_		=				self.cur_size
        self.cur_size += 1
        self.array.append((sys.maxsize, tup[1]))
        self.decrease_key((sys.maxsize, tup[1])   ,		tup[0])







   def lowerCamelCase		( self						:		List[Any]):

        """simple docstring"""


        UpperCAmelCase_		=				self.array[0][1]
        UpperCAmelCase_		=				self.array[self.cur_size - 1]
        self.cur_size -= 1
        self.min_heapify(1)
        del self.pos[min_node]
        return min_node







   def lowerCamelCase		( self						:		Dict   ,		_snake_case						:		Optional[int]):

        """simple docstring"""


        return 2 * i + 1







   def lowerCamelCase		( self						:		Optional[int]   ,		_snake_case						:		Optional[int]):

        """simple docstring"""


        return 2 * i + 2







   def lowerCamelCase		( self						:		Optional[Any]   ,		_snake_case						:		Tuple):

        """simple docstring"""


        return math.floor(i / 2)







   def lowerCamelCase		( self						:		Optional[Any]   ,		_snake_case						:		int   ,		_snake_case						:		Union[str, Any]):

        """simple docstring"""


        UpperCAmelCase_		=				j
        UpperCAmelCase_		=				i
        UpperCAmelCase_		=				self.array[i]
        UpperCAmelCase_		=				self.array[j]
        UpperCAmelCase_		=				temp







   def lowerCamelCase		( self						:		Union[str, Any]   ,		_snake_case						:		Tuple   ,		_snake_case						:		List[Any]):

        """simple docstring"""


        UpperCAmelCase_		=				self.pos[tup[1]]
        # assuming the new_d is atmost old_d
        UpperCAmelCase_		=				(new_d, tup[1])
        while idx > 0 and self.array[self.par(_snake_case)][0] > self.array[idx][0]:
             self.swap(_snake_case   ,		self.par(_snake_case))
             UpperCAmelCase_		=				self.par(_snake_case)







class __snake_case     :







   def __init__( self						:		Optional[int]   ,		_snake_case						:		int):

        """simple docstring"""


        UpperCAmelCase_		=				{}  # To store graph: u -> (v,w)
        UpperCAmelCase_		=				num  # Number of nodes in graph
        # To store the distance from source vertex
        UpperCAmelCase_		=				[0] * self.num_nodes
        UpperCAmelCase_		=				[-1] * self.num_nodes  # To store the path







   def lowerCamelCase		( self						:		List[str]   ,		_snake_case						:		int   ,		_snake_case						:		int   ,		_snake_case						:		Dict):

        """simple docstring"""


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

        # Assuming undirected graph
        if v in self.adjList:
             self.adjList[v].append((u, w))
        else:
             UpperCAmelCase_		=				[(u, w)]







   def lowerCamelCase		( self						:		str):

        """simple docstring"""


        for u in self.adjList:
             print(_snake_case   ,		'''->'''   ,		''' -> '''.join(str(F"""{v}({w})""") for v, w in self.adjList[u]))







   def lowerCamelCase		( self						:		List[str]   ,		_snake_case						:		List[Any]):

        """simple docstring"""


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

        while not q.is_empty():
             UpperCAmelCase_		=				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_		=				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)   ,		_snake_case)
                       UpperCAmelCase_		=				new_dist
                       UpperCAmelCase_		=				u

        # Show the shortest distances from src
        self.show_distances(_snake_case)







   def lowerCamelCase		( self						:		Dict   ,		_snake_case						:		Optional[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 lowerCamelCase		( self						:		List[str]   ,		_snake_case						:		Union[str, Any]   ,		_snake_case						:		Dict):

        """simple docstring"""


        UpperCAmelCase_		=				[]
        UpperCAmelCase_		=				0
        UpperCAmelCase_		=				dest
        # Backtracking from dest to src
        while self.par[temp] != -1:
             path.append(_snake_case)
             if temp != src:
                  for v, w in self.adjList[temp]:
                       if v == self.par[temp]:
                            cost += w
                            break
             UpperCAmelCase_		=				self.par[temp]
        path.append(_snake_case)
        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: '''   ,		_snake_case)


if __name__ == "__main__":
    snake_case_					:					Tuple       						=			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












import math


def   A		(__A  :       int			)  -> float:







     """simple docstring"""


     UpperCAmelCase_		=				math.log(2  ,							10			) * number
     UpperCAmelCase_		=				round((log_number - int(__A			))  ,							15			)

     return difference


def   A		(__A  :       int = 678910			)  -> int:







     """simple docstring"""


     UpperCAmelCase_		=				90
     UpperCAmelCase_		=				0

     UpperCAmelCase_		=				math.log(1.23  ,							10			)
     UpperCAmelCase_		=				math.log(1.24  ,							10			)
     UpperCAmelCase_		=				0

     while position < number:
          UpperCAmelCase_		=				log_difference(__A			)

          if difference >= upper_limit:
               power_iterator += 93

          elif difference < lower_limit:
               power_iterator += 196

          else:
               UpperCAmelCase_		=				power_iterator
               power_iterator += 196
               position += 1

     return previous_power


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    print(f"{solution() = }")






