Score : $1600$ points

Problem Statement

There is a circumference of length $N$. On this circumference, a point whose distance from a certain fixed point, measured in the clockwise direction, is $x$ has the coordinate $x$.

For each integer $i$ ($0 \leq i \leq N-1$), there is a mouse at coordinate $i+0.5$.

Snuke will throw a piece of cheese $N-1$ times. More specifically, he repeats the following $N-1$ times.

• Choose an integer $y$ ($0 \leq y \leq N-1$) randomly, where $y=i$ is chosen with probability $A_i$ percent. This choice is made independently each time.
• Then, throw cheese from the coordinate $y$. The cheese travels in the clockwise direction on the circumference. When the cheese meets a mouse, the following happens.- If the mouse has not eaten cheese:- It eats the cheese with probability $1/2$. The cheese disappears.
  • It does nothing with probability $1/2$.
  • If the mouse has already eaten cheese:- It does nothing.
• If the mouse has not eaten cheese:
• It eats the cheese with probability $1/2$. The cheese disappears.
• It does nothing with probability $1/2$.
• If the mouse has already eaten cheese:
• It does nothing.
• The cheese keeps traveling on the circumference until eaten by some mouse.

After $N-1$ throws of cheese, there will be exactly one mouse that has never eaten cheese. For each $k=0,1,\cdots,N-1$, find the probability that the mouse at coordinate $k+0.5$ ends up not eating cheese, modulo $998244353$.

Constraints

• $1 \leq N \leq 40$
• $0 \leq A_i$
• $\sum_{0 \leq i \leq N-1} A_i = 100$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_0$ $A_1$ $\cdots$ $A_{N-1}$

Output

Print the answers for $k=0,1,\cdots,N-1$ in one line, with spaces in between.

2
0 100

665496236 332748118

$y=1$ is always chosen. When throwing cheese from this point, the following happens.

• With probability $1/2$, the mouse at coordinate $1.5$ eats it.
• With probability $1/4$, the mouse at coordinate $0.5$ eats it.
• With probability $1/8$, the mouse at coordinate $1.5$ eats it.
• With probability $1/16$, the mouse at coordinate $0.5$ eats it.
• $\vdots$

In the end, the mice at coordinates $0.5$ and $1.5$ eat this cheese with probabilities $1/3$ and $2/3$, respectively.

Therefore, they end up not eating cheese with probabilities $2/3$ and $1/3$, respectively.

2
50 50

499122177 499122177

10
1 2 3 4 5 6 7 8 9 55

333507001 91405664 419217284 757959653 974851434 806873643 112668439 378659755 979030842 137048051