def tree_constructor(strArr) -> bool:

parents = {}

children = {}

for pair in strArr:

child, parent = pair.replace("(", "").replace(")", "").split(",")

if parent not in parents:

parents[parent] = []

parents[parent].append(child)

# Check if the parent has more than 2 children (invalid binary tree)

if len(parents[parent]) > 2:

return False

# Check if the child already has a parent (invalid binary tree)

if child in children:

return False

children[child] = parent

rootCount = len(list(filter(lambda parent: all(child not in parents for child in parents[parent]), parents)))

# for parent in parents:

# if parent not in children:

# rootCount += 1

# There should be exactly one root for a valid binary tree

return rootCount == 1