remove

        fn remove(self: *Self, node: *Node) void {
            // rotate the node down to be a leaf of the tree for removal, respecting priorities.
            while (node.children[0] orelse node.children[1]) |_| {
                self.rotate(node, rotate_right: {
                    const right = node.children[1] orelse break :rotate_right true;
                    const left = node.children[0] orelse break :rotate_right false;
                    break :rotate_right (left.priority < right.priority);
                });
            }

            // node is a now a leaf; remove by nulling out the parent's reference to it.
            const link = if (node.parent) |p| &p.children[@intFromBool(p.children[1] == node)] else &self.root;
            assert(link.* == node);
            link.* = null;

            // clean up after ourselves
            node.priority = 0;
            node.parent = null;
            node.children = [_]?*Node{ null, null };
        }