Story

kazuppa, AwashAmityOak, Yu~, and Ruku are getting ready for a Christmas party.

Yu~ is in charge of decorating the Christmas tree. She will decorate the Oak tree that AwashAmityOak bought.

Yu~: "Aren't Christmas trees supposed to be fir trees?"

The work has begun, but Yu~ has started to wonder how many possible decoration patterns there are.

Problem Statement

You are given a tree with $N$ vertices. The vertices and the edges are each numbered $1,2,\dots$ in order, and edge $i$ connects vertices $a_i$ and $b_i$.

Consider painting each vertex of this tree either red, green, or brown. A painted tree is called a Christmas tree if it satisfies the following conditions.

• For each of red, green, and brown, there exist $1$ or more vertices painted that color.
• There is exactly $1$ vertex painted brown.
• No two vertices painted the same color are directly connected by an edge.

How many possible Christmas trees are there?

Since the answer can be very large, output the answer modulo $998244353$.

Here, $2$ Christmas trees are considered different if there is a vertex painted a different color.

Input

$N$
$a_1\ b_1$
$a_2\ b_2$
$\cdots$
$a_{N-1}\ b_{N-1}$

Constraints

• $3 \le N \le 2\times 10^5$
• $1\le a_i < b_i \le N$
• The given graph is a tree.

Output

Print a newline at the end.

Sample

Sample 1

Input

5
1 2
1 3
3 4
1 5

Output

18

For example, the tree painted as shown below is a Christmas tree. (Many other Christmas trees are possible as well.)

10
6 9
1 8
2 7
1 3
2 4
5 10
3 5
1 6
1 2

46