from typing import Set, Optional

class Tree:
    def __init__( self ) -> None:
        self.left  : Optional[ Tree ] = None
        self.right : Optional[ Tree ] = None

def is_tree_rec( root: Tree, visited: Set[ Tree ] ) -> bool:
    if root in visited:
        return False

    visited.add( root )
    result = True

    if root.left is not None:
        result = result and is_tree_rec( root.left, visited )
    if root.right is not None:
        result = result and is_tree_rec( root.right, visited )

    return result

def is_tree( root: Tree ) -> bool:
    return is_tree_rec( root, set() )


import run_tests