There are $N$ people standing in a line, with person $i$ standing at the $i$-th position from the front.

Repeat the following operation until there is only one person left in the line:

-   Remove the person at the front of the line with a probability of $\frac{1}{2}$, otherwise move them to the end of the line.

For each person $i=1,2,\ldots,N$, find the probability that person $i$ is the last person remaining in the line, modulo $998244353$. (All choices to remove or not are random and independent.)

How to find probabilities modulo $998244353$

The probabilities sought in this problem can be proven to always be a rational number. Furthermore, the constraints of this problem guarantee that if the sought probability 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 $z$.

The input is given from Standard Input in the following format:

```
$N$ 
```

Print the answer for people $i=1,2,\ldots,N$, separated by spaces.

-   $2\leq N\leq 3000$
-   All input values are integers.

332748118 665496236

Person 1 will be the last person remaining in the line with probability $\frac{1}{3}$.
Person 2 will be the last person remaining in the line with probability $\frac{2}{3}$.