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 $R$.

Constraints

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

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.

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