### Problem Statement

You are given a tree with $N$ vertices. The vertices are numbered $1$ through $N$, and the $i$-th edge connects vertex $a_i$ and vertex $b_i$.

Solve the following problem for each $x=1,2,\ldots,N$:

-   There are $(2^N-1)$ non-empty subsets $V$ of the tree's vertices. Find the number, modulo $998244353$, of such $V$ that the subgraph induced by $V$ has exactly $x$ connected components.

What is an induced subgraph? Let $S$ be the subset of the vertices of a graph $G$; then the subgraph of $G$ induced by $S$ is a graph whose vertex set is $S$ and whose edge set consists of all edges of $G$ whose both ends are contained in $S$.

### Input

The input is given from Standard Input in the following format:

```
$N$
$a_1$ $b_1$
$\vdots$
$a_{N-1}$ $b_{N-1}$
```

### Output

Print $N$ lines.  
The $i$-th line should contain the answer for $x=i$.

### Constraints

-   $1 \leq N \leq 5000$
-   $1 \leq a_i \lt b_i \leq N$
-   The given graph is a tree.

10
5
0
0

The induced subgraph will have two connected components in the following five cases and one in the others.

• V={1,2,4}
• V={1,3}
• V={1,3,4}
• V={1,4}
• V={2,4}