Problem Statement

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.

Input

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}

Output

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:
$E_1 E_2 \ldots E_N$

Constraints

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

Sample Input 1

5
1 2
4 3
5 3
1 4

Sample Output 1

698771048 698771048 964969543 964969543 133099248

We call a team formed by player $x_1, player x_2, \ldots, player x_k$ as team $\lbrace x_1, x_2, \ldots, x_k \rbrace$.

• The first match is played by team $\lbrace 1 \rbrace$, with player 1, and team $\lbrace 2 \rbrace$, with player $2. Team \lbrace 1 \rbrace$ wins with probability $\frac{1}{2}$, and team $\lbrace 2 \rbrace$ wins with probability $\frac{1}{2}.$ Then, the two teams are combined into $a single team \lbrace 1, 2 \rbrace$.
• The second match is played by team $\lbrace 4 \rbrace$, with player 4, and team $\lbrace 3 \rbrace$, with player $3. Team \lbrace 4 \rbrace$ wins with probability $\frac{1}{2}$, and team $\lbrace 3 \rbrace$ wins with probability $\frac{1}{2}.$ Then, the two teams are combined into $a single team \lbrace 3, 4 \rbrace$.
• The third match is played by team $\lbrace 5 \rbrace$, with player 5, and team $\lbrace 3, 4 \rbrace$, with player $3. Team \lbrace 5 \rbrace$ wins with probability $\frac{1}{3}$, and team $\lbrace 3, 4 \rbrace$ wins with probability $\frac{2}{3}.$ Then, the two teams are combined into $a single team \lbrace 3, 4, 5 \rbrace$.
• The fourth match is played by team $\lbrace 1, 2 \rbrace$, with player 1, and team $\lbrace 3, 4, 5 \rbrace$, with player $4. Team \lbrace 1, 2 \rbrace$ wins with probability $\frac{2}{5}$, and team $\lbrace 3, 4, 5 \rbrace$ wins with probability $\frac{3}{5}.$ Then, the two teams are combined into $a single team \lbrace 1, 2, 3, 4, 5 \rbrace$.

The expected numbers of times the teams with players 1, 2, 3, 4, 5 win throughout the tournament, E_1, E_2, E_3, E_4, E_5, are $\frac{9}{10}, \frac{9}{10}, \frac{53}{30}, \frac{53}{30}, \frac{14}{15},$ respectively.

Sample Input 2

15
9 2
8 10
13 6
12 11
7 10
4 10
14 2
5 4
1 15
15 2
6 9
8 11
6 3
2 8

Sample Output 2

43970290 310168785 806914186 501498951 950708909 272140427 335124893 168750835 310168785 168750835 280459129 280459129 272140427 476542843 43970290

见题面 Input 部分

见题面 Output 部分