Define the unique ornamental coloring of a rooted tree(^{\text{∗}}) as the following vertex coloring: A vertex (v) is colored white if the number of vertices in the subtree(^{\text{†}}) rooted at (v) is even; Otherwise, (v) is colored black. On his quest to conquer a forest of Christmas trees, Yuuki encountered an ornamentally colored tree (T) with (n) vertices labeled from (1) to (n), rooted at vertex (1). Yuuki considers the tree conquered if and only if at least one of the following conditions holds: There are no white vertices in the tree, or There exists some vertex (v) such that all white vertices lie on the simple path from the root (1) to (v). To conquer the tree, Yuuki can apply the following operation on (T) an arbitrary number of times (possibly zero): First, choose a vertex (w) that is colored white and is not the root of (T). Let (p_w) be the parent of (w). Then, remove the edge connecting (p_w) and (w), and add an edge between any two vertices such that (T) remains a tree. Finally, recolor the vertices of (T) such that it is ornamentally colored. Note that (T) is always rooted at vertex (1). Compute the number of distinct(^{\text{‡}}) conquered trees that Yuuki can construct by applying the above operation an arbitrary number of times on (T). Since the answer may be large, output it modulo (998\,244\,353). Note that Yuuki cannot stop midway through an operation (in particular, he must recolor the tree before checking if it is conquered ). Additionally, Yuuki is allowed to apply the operation even if the tree is already conquered . (^{\text{∗}})A tree is a connected graph without cycles. (^{\text{†}})A subtree of vertex (v) is the subgraph of (v), all its descendants, and all the edges between them. (^{\text{‡}})Two trees are considered distinct if and only if there exists a pair of vertices such that there is an edge