$N$ players, player $1$, player $2$, ..., player $N$, participate in a game tournament. Just before the tournament starts, each player forms a one-person team, so there are $N$ teams in total.

The tournament has a total of $N-1$ matches. In each match, two different teams are chosen. One team goes first, and the other goes second. Each match will result in exactly one team winning. Specifically, for each $i = 1, 2, \ldots, N-1$, the $i$-th match proceeds as follows.

-   The team with player $p_i$ goes first, and the team with player $q_i$ goes second.
-   Let $a$ and $b$ be the numbers of players in the first and second teams, respectively. The first team wins with probability $\frac{a}{a+b}$, and the second team wins with probability $\frac{b}{a+b}$.
-   Then, the two teams are combined into a single team.

The result of each match is independent of those of the others.

For each of the $N$ players, print the expected number of times the team with that player wins throughout the tournament, modulo $998244353$.

How to print an expected value modulo $998244353$

It can be proved that the sought expected value is always rational. Also, the constraints of this problem guarantee that if the sought expected value is expressed as an irreducible fraction $\frac{y}{x}$, then $x$ is not divisible by $998244353$.

Now, there is a unique integer $z$ between $0$ and $998244352$, inclusive, such that $xz \equiv y \pmod{998244353}$. Report this $z$.

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

```
$N$
$p_1$ $q_1$
$p_2$ $q_2$
$\vdots$
$p_{N-1}$ $q_{N-1}$
```

For each $i = 1, 2, \ldots, N$, print $E_i$, the expected number, modulo $998244353$, of times the team with player $i$ wins throughout the tournament, separated by spaces, in the following format:

```
$E_1$ $E_2$ $\ldots$ $E_N$
```

-   $2 \leq N \leq 2 \times 10^5$
-   $1 \leq p_i, q_i \leq N$
-   Just before the $i$\-th match, player $p_i$ and player $q_i$ belong to different teams.
-   All input values are integers.

698771048 698771048 964969543 964969543 133099248