'''simple docstring'''

def __a (	__lowerCamelCase			:						list[int] ,		__lowerCamelCase			:						list[int]				)	->							tuple[float, float]:
      '''simple docstring'''


      if not len(__lowerCamelCase				) == len(__lowerCamelCase				) == 3:
            raise ValueError("Please enter a valid equation."				)
      if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
            raise ValueError("Both a & b of two equations can't be zero."				)

      # Extract the coefficients
      lowercase_ ,							lowercase_ ,							lowercase_     =      equationa
      lowercase_ ,							lowercase_ ,							lowercase_     =      equationa

      # Calculate the determinants of the matrices
      lowercase_     =      aa * ba - aa * ba
      lowercase_     =      ca * ba - ca * ba
      lowercase_     =      aa * ca - aa * ca

      # Check if the system of linear equations has a solution (using Cramer's rule)
      if determinant == 0:
            if determinant_x == determinant_y == 0:
                  raise ValueError("Infinite solutions. (Consistent system)"				)
            else:
                  raise ValueError("No solution. (Inconsistent system)"				)
      else:
            if determinant_x == determinant_y == 0:
                  # Trivial solution (Inconsistent system)
                  return (0.0, 0.0)
            else:
                  lowercase_     =      determinant_x / determinant
                  lowercase_     =      determinant_y / determinant
                  # Non-Trivial Solution (Consistent system)
                  return (x, y)







'''simple docstring'''

# Author: OMKAR PATHAK, Nwachukwu Chidiebere

# Use a Python dictionary to construct the graph.
from __future__ import annotations

from pprint import pformat
from typing import Generic, TypeVar

lowerCAmelCase_ : Dict						  =      TypeVar("T")





class 							lowercase						(						Generic[T] ):


   def __init__(   self				:	int   ,		__lowerCAmelCase				:	bool = True)      ->					None:
         lowercase_     =      {}  # dictionary of lists
         lowercase_     =      directed


   def __UpperCAmelCase       (   self				:	int   ,		__lowerCAmelCase				:	T   ,		__lowerCAmelCase				:	T)      ->					GraphAdjacencyList[T]:

         if not self.directed:  # For undirected graphs
               # if both source vertex and destination vertex are both present in the
               # adjacency list, add destination vertex to source vertex list of adjacent
               # vertices and add source vertex to destination vertex list of adjacent
               # vertices.
               if source_vertex in self.adj_list and destination_vertex in self.adj_list:
                     self.adj_list[source_vertex].append(__lowerCAmelCase)
                     self.adj_list[destination_vertex].append(__lowerCAmelCase)
               # if only source vertex is present in adjacency list, add destination vertex
               # to source vertex list of adjacent vertices, then create a new vertex with
               # destination vertex as key and assign a list containing the source vertex
               # as it's first adjacent vertex.
               elif source_vertex in self.adj_list:
                     self.adj_list[source_vertex].append(__lowerCAmelCase)
                     lowercase_     =      [source_vertex]
               # if only destination vertex is present in adjacency list, add source vertex
               # to destination vertex list of adjacent vertices, then create a new vertex
               # with source vertex as key and assign a list containing the source vertex
               # as it's first adjacent vertex.
               elif destination_vertex in self.adj_list:
                     self.adj_list[destination_vertex].append(__lowerCAmelCase)
                     lowercase_     =      [destination_vertex]
               # if both source vertex and destination vertex are not present in adjacency
               # list, create a new vertex with source vertex as key and assign a list
               # containing the destination vertex as it's first adjacent vertex also
               # create a new vertex with destination vertex as key and assign a list
               # containing the source vertex as it's first adjacent vertex.
               else:
                     lowercase_     =      [destination_vertex]
                     lowercase_     =      [source_vertex]
         else:  # For directed graphs
               # if both source vertex and destination vertex are present in adjacency
               # list, add destination vertex to source vertex list of adjacent vertices.
               if source_vertex in self.adj_list and destination_vertex in self.adj_list:
                     self.adj_list[source_vertex].append(__lowerCAmelCase)
               # if only source vertex is present in adjacency list, add destination
               # vertex to source vertex list of adjacent vertices and create a new vertex
               # with destination vertex as key, which has no adjacent vertex
               elif source_vertex in self.adj_list:
                     self.adj_list[source_vertex].append(__lowerCAmelCase)
                     lowercase_     =      []
               # if only destination vertex is present in adjacency list, create a new
               # vertex with source vertex as key and assign a list containing destination
               # vertex as first adjacent vertex
               elif destination_vertex in self.adj_list:
                     lowercase_     =      [destination_vertex]
               # if both source vertex and destination vertex are not present in adjacency
               # list, create a new vertex with source vertex as key and a list containing
               # destination vertex as it's first adjacent vertex. Then create a new vertex
               # with destination vertex as key, which has no adjacent vertex
               else:
                     lowercase_     =      [destination_vertex]
                     lowercase_     =      []

         return self


   def __repr__(   self				:	str)      ->					str:
         return pformat(self.adj_list)






