


from __future__ import annotations

from typing import Generic, TypeVar

snake_case__			 =						TypeVar('''T''')


class 					lowerCAmelCase_ (       Generic[T]):




      def __init__(	self						:   Any   ,     __A						:   T						)      ->Optional[int]:






         """simple docstring"""






         a__ :Optional[int]						  =    data
         a__ :str						  =    self
         a__ :str						  =    0






class 					lowerCAmelCase_ (       Generic[T]):




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






         """simple docstring"""






         a__ :Tuple						  =    {}




      def  _snake_case					(	self						:   str   ,     __A						:   T						)      ->Union[str, Any]:






         """simple docstring"""






         a__ :str						  =    DisjointSetTreeNode(_A						)




      def  _snake_case					(	self						:   List[Any]   ,     __A						:   T						)      ->List[str]:






         """simple docstring"""






         a__ :Optional[int]						  =    self.map[data]
         if elem_ref != elem_ref.parent:
            a__ :Dict						  =    self.find_set(elem_ref.parent.data						)
         return elem_ref.parent




      def  _snake_case					(	self						:   List[Any]   ,     __A						:   DisjointSetTreeNode[T]   ,     __A						:   DisjointSetTreeNode[T]						)      ->Tuple:






         """simple docstring"""






         if nodea.rank > nodea.rank:
            a__ :Dict						  =    nodea
         else:
            a__ :List[str]						  =    nodea
            if nodea.rank == nodea.rank:
               nodea.rank += 1






      def  _snake_case					(	self						:   List[Any]   ,     __A						:   T   ,     __A						:   T						)      ->Any:






         """simple docstring"""






         self.link(self.find_set(_A						)   ,     self.find_set(_A						)						)






class 					lowerCAmelCase_ (       Generic[T]):




      def __init__(	self						:   Any						)      ->str:






         """simple docstring"""






         a__ :int						  =    {}




      def  _snake_case					(	self						:   Optional[int]   ,     __A						:   T						)      ->str:






         """simple docstring"""






         if node not in self.connections:
            a__ :List[Any]						  =    {}




      def  _snake_case					(	self						:   Tuple   ,     __A						:   T   ,     __A						:   T   ,     __A						:   int						)      ->Optional[int]:






         """simple docstring"""






         self.add_node(_A						)
         self.add_node(_A						)
         a__ :Tuple						  =    weight
         a__ :Union[str, Any]						  =    weight






      def  _snake_case					(	self						:   Optional[int]						)      ->int:






         """simple docstring"""






         a__ :List[str]						  =    []
         a__ :int						  =    set()
         for start in self.connections:
            for end in self.connections[start]:
               if (start, end) not in seen:
                  seen.add((end, start)						)
                  edges.append((start, end, self.connections[start][end])						)
         edges.sort(key=lambda __A						: x[2]						)

         # creating the disjoint set
         a__ :Union[str, Any]						  =    DisjointSetTree[T]()
         for node in self.connections:
            disjoint_set.make_set(_A						)

         # MST generation
         a__ :str						  =    0
         a__ :Tuple						  =    0
         a__ :Optional[Any]						  =    GraphUndirectedWeighted[T]()
         while num_edges < len(self.connections						) - 1:
            a__  ,  a__  ,  a__ :Dict						  =    edges[index]
            index += 1
            a__ :List[Any]						  =    disjoint_set.find_set(_A						)
            a__ :List[str]						  =    disjoint_set.find_set(_A						)
            if parent_u != parent_v:
               num_edges += 1
               graph.add_edge(_A   ,     _A   ,     _A						)
               disjoint_set.union(_A   ,     _A						)
         return graph






def 				lowerCamelCase__	(      a	:   int	,  a	:   int				)    ->	Any:





			"""simple docstring"""
			# "extended trapezoidal rule"
			# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
			a__ :Optional[int]						  =    (boundary[1] - boundary[0]) / steps
			a__ :str						  =    boundary[0]
			a__ :Optional[int]						  =    boundary[1]
			a__ :str						  =    make_points(a	,  a	,  a				)
			a__ :Any						  =    0.0
			y += (h / 2.0) * f(a				)
			for i in x_i:
						# print(i)
						y += h * f(a				)
			y += (h / 2.0) * f(a				)
			return y


def 				lowerCamelCase__	(      a	:   Any	,  a	:   str	,  a	:   Dict				)    ->	int:





			"""simple docstring"""
			a__ :Union[str, Any]						  =    a + h
			while x < (b - h):
						yield x
						a__ :str						  =    x + h


def 				lowerCamelCase__	(      a	:   Optional[int]				)    ->	List[Any]:  # enter your function here





			"""simple docstring"""
			a__ :Tuple						  =    (x - 0) * (x - 0)
			return y


def 				lowerCamelCase__	(      )    ->	List[str]:





			"""simple docstring"""
			a__ :Optional[Any]						  =    0.0  # Lower bound of integration
			a__ :Optional[Any]						  =    1.0  # Upper bound of integration
			a__ :List[str]						  =    1_0.0  # define number of steps or resolution
			a__ :int						  =    [a, b]  # define boundary of integration
			a__ :str						  =    method_a(a	,  a				)
			print(F'''y = {y}'''				)


if __name__ == "__main__":
		main()


