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 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