
Score : 1100 points
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.
Constraints
 3 \le N \le 2 \times 10^5 
 1 \le a_i, b_i \le N 
The given graph is a tree.
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.
Sample Input 16
1 6
2 1
5 2
3 4
2 3
Sample Output 13
For example, adding the edges (1, 5), (3, 5) in G satisfies the conditions.
Sample Input 23
1 2
2 3
Sample Output 21
The only graph H that satisfies the conditions is G.
Sample Input 39
1 2
2 3
4 2
1 7
6 1
2 5
5 9
6 8
Sample Output 327
Sample Input 419
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 478732
