Depths

Your task is to compute the sum of the depths of all nodes in a given tree.

In a file depths.py, implement a function count that returns the sum of depths.

class Node:
    def __init__(self, value, children=[]):
        self.value = value
        self.children = children

def count(node):
    # TODO

if __name__ == "__main__":
    tree = Node(1, [
               Node(2),
               Node(3, [Node(4, [Node(5), Node(6)])]),
               Node(7, [Node(8), Node(9)])
           ])

    print(count(tree)) # 15