Problem Statement

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.

Input

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

Output

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

Constraints

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

Sample Input 1

2

Sample Output 1

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 $\frac{2}{3}$.

Sample Input 2

5

Sample Output 2

235530465 792768557 258531487 238597268 471060930

见题面 Input 部分

见题面 Output 部分