class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def max_depth(root: TreeNode) -> int:
    # 递归终止条件：空节点深度为0
    if not root:
        return 0
    # 待填写逻辑
    ________