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.

Examples

Input

6
1 6
2 1
5 2
3 4
2 3

Output

3

Input

3
1 2
2 3

Output

1

Input

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

Output

27

Input

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

Output

78732

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