Problem Statement

We have a tree with $N$ vertices, numbered $1, \ldots, N$. For each $i=1,\ldots,N-1$, the $i$-th edge connects Vertex $a_i$ and Vertex $b_i$. An operation on this tree when at most one piece is put on each vertex is defined as follows.

• Simultaneously move every piece to one of the vertices adjacent to the one occupied by the piece.

An operation is said to be good when the conditions below are satisfied.

• Each edge is traversed by at most one piece.
• Each vertex will be occupied by at most one piece after the operation.

Takahashi will put a piece on one or more vertices of his choice. Among the $2^N-1$ ways to put pieces, find the number of ones that satisfy the condition below, modulo $998244353$.

• For every non-negative integer $K$, the following holds.
• It is possible to perform a good operation $K$ times.
  • Let $S_K$ be the set of vertices occupied by pieces just after $K$ good operations. Then, $S_K$ is unique.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq a_i \lt b_i \leq N$
• The given graph is a tree.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
\vdots
a_{N-1} b_{N-1}

Output

Print the answer.