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.

• 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.
How to represent a probability modulo 998244353

We can prove that each probability in question is always a rational number. Additionally, under the Constraints of this problem, when that number is represented as an irreducible fraction $\frac{P}{Q}$, we can also prove that $Q \neq 0 \pmod{998244353}.$ Thus, there is a unique integer R such that $R \times Q \equiv P \pmod{998244353}, 0 \leq R < 998244353.$ Answer with this R.

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.

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.

Sample Input 1

2
0 100

Sample Output 1

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.

Sample Input 2

2
50 50

Sample Output 2

499122177 499122177

Sample Input 3

10
1 2 3 4 5 6 7 8 9 55

Sample Output 3

333507001 91405664 419217284 757959653 974851434 806873643 112668439 378659755 979030842 137048051

见题面 Input 部分

见题面 Output 部分