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 $R$.

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.