





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
_UpperCamelCase    =	{
    '''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  lowerCAmelCase__(		lowercase    :      List[Any]			)	->      int:
  __snake_case				:			Tuple            =    {node: {node} for node in graph}

  __snake_case				:			Optional[Any]            =    {node: graph[node][:] for node in graph}

  while len(SCREAMING_SNAKE_CASE_			) > 2:
    # Choose a random edge.
    __snake_case				:			Any            =    random.choice(list(graph_copy.keys()			)			)
    __snake_case				:			List[Any]            =    random.choice(graph_copy[u]			)

    # Contract edge (u, v) to new node uv
    __snake_case				:			Union[str, Any]            =    u + v
    __snake_case				:			Tuple            =    list(set(graph_copy[u] + graph_copy[v]			)			)
    uv_neighbors.remove(SCREAMING_SNAKE_CASE_			)
    uv_neighbors.remove(SCREAMING_SNAKE_CASE_			)
    __snake_case				:			Any            =    uv_neighbors
    for neighbor in uv_neighbors:
      graph_copy[neighbor].append(SCREAMING_SNAKE_CASE_			)

    __snake_case				:			Union[str, Any]            =    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(SCREAMING_SNAKE_CASE_			)
      if v in graph_copy[neighbor]:
        graph_copy[neighbor].remove(SCREAMING_SNAKE_CASE_			)

    # Find cutset.
  __snake_case				:			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))








_UpperCamelCase    =	[chr(i) for i in range(32, 126)]
_UpperCamelCase    =	list(range(len(alphabets)))
_UpperCamelCase    =	list(range(len(alphabets)))
_UpperCamelCase    =	list(range(len(alphabets)))
_UpperCamelCase    =	list(reversed(range(len(alphabets))))
_UpperCamelCase    =	[]
_UpperCamelCase    =	_UpperCamelCase    =	_UpperCamelCase    =	0







def  lowerCAmelCase__(		)	->      int:
  global gear_one_pos
  global gear_two_pos
  global gear_three_pos
  __snake_case				:			int            =    gear_one[0]
  gear_one.append(lowercase			)
  del gear_one[0]
  gear_one_pos += 1
  if gear_one_pos % int(len(lowercase			)			) == 0:
    __snake_case				:			List[str]            =    gear_two[0]
    gear_two.append(lowercase			)
    del gear_two[0]
    gear_two_pos += 1
    if gear_two_pos % int(len(lowercase			)			) == 0:
      __snake_case				:			Any            =    gear_three[0]
      gear_three.append(lowercase			)
      del gear_three[0]
      gear_three_pos += 1







def  lowerCAmelCase__(		lowercase    :      Tuple			)	->      Union[str, Any]:
  __snake_case				:			Union[str, Any]            =    alphabets.index(lowercase			)
  __snake_case				:			Tuple            =    gear_one[target]
  __snake_case				:			Union[str, Any]            =    gear_two[target]
  __snake_case				:			int            =    gear_three[target]
  __snake_case				:			Optional[int]            =    reflector[target]
  __snake_case				:			Union[str, Any]            =    gear_three.index(lowercase			)
  __snake_case				:			Optional[Any]            =    gear_two.index(lowercase			)
  __snake_case				:			int            =    gear_one.index(lowercase			)
  code.append(alphabets[target]			)
  rotator()


if __name__ == "__main__":
     _UpperCamelCase    =	list(input('''Type your message:\n'''))
     while True:
          try:
               _UpperCamelCase    =	int(input('''Please set token:(must be only digits)\n'''))
               break
          except Exception as error:
               print(error)
     for _ in range(token):
          rotator()
     for j in decode:
          engine(j)
     print('''\n''' + ''''''.join(code))
     print(
         F'''\nYour Token is {token} please write it down.\nIf you want to decode '''
         '''this message again you should input same digits as token!'''
     )

