Problem Statement

We have a tree G with N vertices numbered 1 to N.
The i-th edge of G connects Vertex a_i and Vertex b_i.
Consider adding zero or more edges in G, and let H be the graph resulted.
Find the number of graphs H that satisfy the following conditions, modulo 998244353.

• H does not contain self-loops or multiple edges.
• The diameters of G and H are equal.
• For every pair of vertices in H that is not directly connected by an edge, the addition of an edge directly connecting them would reduce the diameter of the graph.

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.

Constraints

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

Sample Input 1

6
1 6
2 1
5 2
3 4
2 3

Sample Output 1

3

For example, adding the edges (1, 5), (3, 5) in G satisfies the conditions.

Sample Input 2

3
1 2
2 3

Sample Output 2

1

The only graph H that satisfies the conditions is G.

Sample Input 3

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

Sample Output 3

27

Sample Input 4

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

Sample Output 4

78732

见题面 Input 部分

见题面 Output 部分