from json import dumps

class Tree(object):

def __init__(self, label, children=[]):

self.label = label

self.children = children

def __dict__(self):

return {self.label: [c.__dict__() for c in sorted(self.children)]}

def __str__(self, indent=None):

return dumps(self.__dict__(), indent=indent)

def __lt__(self, other):

return self.label < other.label

def __eq__(self, other):

return self.__dict__() == other.__dict__()

def from_pov(self, from_node):

if self.label == from_node:

return self

for i in range(len(self.children)):

if self.children[i].label == from_node:

x = self.children[i]

current = i

y= Tree(self.label)

if self.children:

for j in range(len(self.children)):

if j != current:

y.children = y.children+ [self.children[j]]

x.children = x.children + [y]

return x

else:

try:

x = self.children[i].from_pov(from_node)

current = i

y= Tree(self.label)

if self.children:

for j in range(len(self.children)):

if j != current:

y.children = y.children+ [self.children[j]]

x.add_tree(self.children[current].label,y)

return x

except ValueError :

pass

else:

raise ValueError('ValueError')

def add_tree(self,label, subtree):

for i in range(len(self.children)):

if label == self.children[i].label:

self.children[i].children = self.children[i].children + [subtree]

else:

z = self.children[i].add_tree(label,subtree)

if z is None:

continue

def path_to(self, from_node, to_node):

node_tree = self.from_pov(from_node)

for child in node_tree.children:

if child.label == to_node:

return [from_node,child.label]

else:

try:

y= child.path_to(child.label,to_node)

except ValueError:

pass

else:

return [from_node]+ y

else:

raise ValueError('ValueError')