Problem Statement

For an undirected tree t, let us define a rational number f(t) as follows.

• Let n be the number of vertices in t.
• If n=1: Let f(t)=1.
• If $n \geq 2$:
• For an edge e in t, we denote by t_x(e) and t_y(e) the two trees that result from deleting e from t (in arbitrary order).
• Let $f(t)=(\sum_{e \in$ $t} f(t_x(e)) \times f(t_y(e)))/n$.

You are given a tree T with N vertices numbered 1 to N.
The i-th edge connects Vertex A_i and Vertex B_i.
Find the value $f(T) \text{mod }{998244353}$.
What is $a rational number \text{mod }{998244353}$?

Under the Constraints of this problem, when the sought rational number is represented as $\frac{P}{Q}$, it can be proved that $Q \neq 0 \pmod{998244353}.$ Therefore, there is a unique integer R such that $R \times Q \equiv P \pmod{998244353}, 0 \leq R < 998244353.$ Find this R.

Input

Input is given from Standard Input in the following format:
N
A_1 B_1
A_2 B_2
$\vdots$
A_{N-1} B_{N-1}

Output

Print the answer.

Constraints

• $2 \leq N \leq 5000$
• $1 \leq A_i,B_i \leq N$
• The given graph is a tree.

Sample Input 1

2
1 2

Sample Output 1

499122177

We have f(T)=1/2.

Sample Input 2

3
1 2
2 3

Sample Output 2

332748118

We have f(T)=1/3.

Sample Input 3

4
1 2
2 3
3 4

Sample Output 3

103983787

Sample Input 4

10
4 5
1 9
6 1
8 4
5 9
4 7
3 10
5 2
4 3

Sample Output 4

462781191

见题面 Input 部分

见题面 Output 部分