Problem Statement

Given is a tree with N vertices numbered 1 through N.
The i-th edge connects Vertices a_i and b_i.
Snuke will label each vertex with 0 or 1 and each edge with AND or OR.
Among the 2^{2N-1} ways to label the vertices and edges, find the number of ways that satisfy the following condition, modulo 998244353.
Condition: There exists a sequence of N-1 operations ending up with one vertex labeled 1, where each operation consists of the steps below.

• Choose one edge and contract it. Here, let x and y be the labels of the erased vertices and $\mathrm{op}$ be the label of the erased edge.
• If $\mathrm{op}$ is AND, label the new vertex with $\mathrm{AND}(x,y)$; if $\mathrm{op}$ is OR, label the new vertex with $\mathrm{OR}(x,y)$.

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 number of ways to label the tree that satisfy the condition in Problem Statement, modulo 998244353.

Constraints

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

Sample Input 1

2
1 2

Sample Output 1

4

Sample Input 2

20
7 3
20 18
16 12
7 2
10 5
18 16
16 3
4 11
7 15
8 1
6 1
12 13
15 5
19 17
7 1
9 8
7 17
16 14
11 7

Sample Output 2

283374562

• Remember to print the count modulo 998244353.

见题面 Input 部分

见题面 Output 部分