Stamp Rally

You are in charge of $N$ lodges and the road that connects each lodge. Each lodge has a number from 1 to $N$. There are $N-1$ paths in total. All paths can be traveled in both directions. Also, from any lodge, you can reach other lodges by taking some of the paths.

You decide to start a stamp rally by placing stamps at all the lodges so that the lodge visitors can enjoy themselves. The rules of this stamp rally are as follows.

• Visitors choose a number of mountain lodges. At this time, the number of lodges that can be chosen is from 2 to $N$. After that, they move to one of the lodges they have chosen and start the stamp rally from there.
• During the stamp rally, visitors move between the lodges along a path. They will visit all the lodges that they pass during their journey and stamp them there.
• If the user visits a lodge that has already been stamped, the stamp rally fails and ends at that point.
• When you have visited all the lodges you have chosen, the stamp rally will be successful and you will receive a prize.

In order to make the stamp rally successful, users need to choose the correct route to visit the mountain lodges. However, depending on how the mountain lodges are chosen, it will not be possible to succeed no matter how the route is chosen. Therefore, we decided to only allow people to choose mountain lodges that would allow them to successfully complete the stamp rally. How many such combination of mountain lodges are there?

You are given the information on the number of lodges and the paths that connect the lodges directly to each other will be given. When choosing from 2 to $N$ mountain lodges each, find the number of ways to choose mountain lodges that would allow the stamp rally to be successful for each number of lodges chosen.

Input

The input is given in the following form.

$N$
$s_1$ $t_1$
$s_2$ $t_2$
:
$s_{N-1}$ $t_{N-1}$

In the first line, the number of lodges $N$ ($2 \leq N \leq 200,000$) is given. In the following $N-1$ lines, the information of the path directly connecting the two lodges is given. $s_i$ and $t_i$ ($1 \leq s_i < t_i \leq N$) are the numbers of the two lodges connected by the $i$-th path. For any two lodges, there should be no more than one path that directly connects them.

Output

The output consists of $N-1$ lines, where the $i$-th line is the number of ways to choose lodge that would make the stamp rally successful if $i+1$ lodges were chosen. Divide the answer by 998,244,353 and output the remainder.

 

Sample Input and Output

Sample Input

5
1 2
2 3
3 4
3 5

Sample Output

10
8
2
0

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