Subtrees

Your task is to build a list that contains the subtree sizes for all the nodes in a tree from the smallest to the largest.

For example, in the tree below, the desired list is $[1, 1, 1, 1, 2, 3, 7]$. The tree has four leaves with a subtree size of $1$. The node $2$ has a subtree of size $2$, the node $4$ has a subtree of size $3$, and the node $1$ has a subtree of size $7$.

In a file subtrees.py, implement the function count_subtrees that takes a reference to the root of a tree as parameter and returns the list of subtree sizes.

class Node:
    def __init__(self, value, children=None):
        self.value = value
        self.children = children if children else []

    def __repr__(self):
        if self.children == []:
            return f"Node({self.value})"
        else:
            return f"Node({self.value}, {self.children})"

def count_subtrees(node):
    # TODO

if __name__ == "__main__":
    tree1 = Node(1, [Node(4, [Node(3), Node(7)]),
                     Node(5),
                     Node(2, [Node(6)])])
    print(count_subtrees(tree1)) # [1, 1, 1, 1, 2, 3, 7]

    tree2 = Node(1, [Node(2, [Node(3, [Node(4)])])])
    print(count_subtrees(tree2)) # [1, 2, 3, 4]

    tree3 = Node(1, [Node(2), Node(3), Node(4)])
    print(count_subtrees(tree3)) # [1, 1, 1, 4]