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.