code: 
  
  from __future__ import annotations
  
  import random
  
  # Adjacency list representation of this graph:
  # https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
  __A   :     Optional[int]      =			{
      '''1''': ['''2''', '''3''', '''4''', '''5'''],
      '''2''': ['''1''', '''3''', '''4''', '''5'''],
      '''3''': ['''1''', '''2''', '''4''', '''5''', '''10'''],
      '''4''': ['''1''', '''2''', '''3''', '''5''', '''6'''],
      '''5''': ['''1''', '''2''', '''3''', '''4''', '''7'''],
      '''6''': ['''7''', '''8''', '''9''', '''10''', '''4'''],
      '''7''': ['''6''', '''8''', '''9''', '''10''', '''5'''],
      '''8''': ['''6''', '''7''', '''9''', '''10'''],
      '''9''': ['''6''', '''7''', '''8''', '''10'''],
      '''10''': ['''6''', '''7''', '''8''', '''9''', '''3'''],
  }
  def 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase				)					-> set[tuple[str, str]]:
  
  
  
      '''simple docstring'''
  
  
  
  
  
  
      lowerCAmelCase				:			List[Any]    			=      {node: {node} for node in graph}
  
      lowerCAmelCase				:			List[str]    			=      {node: graph[node][:] for node in graph}
  
      while len(_UpperCAmelCase				) > 2:
          # Choose a random edge.
          lowerCAmelCase				:			List[Any]    			=      random.choice(list(graph_copy.keys()				)				)
          lowerCAmelCase				:			Any    			=      random.choice(graph_copy[u]				)
  
          # Contract edge (u, v) to new node uv
          lowerCAmelCase				:			str    			=      u + v
          lowerCAmelCase				:			Optional[Any]    			=      list(set(graph_copy[u] + graph_copy[v]				)				)
          uv_neighbors.remove(_UpperCAmelCase				)
          uv_neighbors.remove(_UpperCAmelCase				)
          lowerCAmelCase				:			Dict    			=      uv_neighbors
          for neighbor in uv_neighbors:
              graph_copy[neighbor].append(_UpperCAmelCase				)
  
          lowerCAmelCase				:			int    			=      set(contracted_nodes[u].union(contracted_nodes[v]				)				)
  
          # Remove nodes u and v.
          del graph_copy[u]
          del graph_copy[v]
          for neighbor in uv_neighbors:
              if u in graph_copy[neighbor]:
                  graph_copy[neighbor].remove(_UpperCAmelCase				)
              if v in graph_copy[neighbor]:
                  graph_copy[neighbor].remove(_UpperCAmelCase				)
  
      # Find cutset.
      lowerCAmelCase				:			str    			=      [contracted_nodes[node] for node in graph_copy]
      return {
          (node, neighbor)
          for node in groups[0]
          for neighbor in graph[node]
          if neighbor in groups[1]
      }
  
  
  if __name__ == "__main__":
   print(partition_graph(TEST_GRAPH))
  
  
  
  
  
  
style_context: 
  
  from __future__ import annotations
  def 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase				)					-> set[int]:
  
  
  
      '''simple docstring'''
  
  
  
  
  
  
      lowerCAmelCase				:			List[str]    			=      {1}
      lowerCAmelCase				:			int    			=      [1]
      for _ in range(2,      depth + 1				):
          lowerCAmelCase				:			str    			=      [*previous_coefficients, 0]
          lowerCAmelCase				:			Optional[int]    			=      [0, *previous_coefficients]
          lowerCAmelCase				:			Tuple    			=      []
          for x, y in zip(_UpperCAmelCase,      _UpperCAmelCase				):
              coefficients.add(x + y				)
              previous_coefficients.append(x + y				)
      return coefficients
  def 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase				)					-> set[int]:
  
  
  
      '''simple docstring'''
  
  
  
  
  
  
      lowerCAmelCase				:			str    			=      set()
      for number in unique_coefficients:
          lowerCAmelCase				:			Dict    			=      2
          lowerCAmelCase				:			Tuple    			=      number
          while divisor**2 <= copy_number:
              lowerCAmelCase				:			List[str]    			=      0
              while copy_number % divisor == 0:
                  copy_number //= divisor
                  multiplicity += 1
              if multiplicity >= 2:
                  non_squarefrees.add(_UpperCAmelCase				)
                  break
              divisor += 1
  
      return unique_coefficients.difference(_UpperCAmelCase				)
  def 		SCREAMING_SNAKE_CASE__				(							_UpperCAmelCase = 51				)					-> int:
  
  
  
      '''simple docstring'''
  
  
  
  
  
  
      lowerCAmelCase				:			int    			=      get_pascal_triangle_unique_coefficients(_UpperCAmelCase				)
      lowerCAmelCase				:			Optional[int]    			=      get_squarefrees(_UpperCAmelCase				)
      return sum(_UpperCAmelCase				)
  
  
  if __name__ == "__main__":
   print(F'{solution() = }')
  
  
  
  
  
  