Little N has recently learned about MEX. MEX (Minimum Excluded) refers to the smallest non-negative integer that does not appear in an array. For example: $\operatorname{{MEX}}([3, 1, 0]) = 2$, $\operatorname{{MEX}}([2, 2, 1]) = 0$, $\operatorname{{MEX}}([0, 3, 1, 2]) = 4$. Little N defines that for a non-negative integer array of length $k$, $[b_1, b_2, \dots, b_k]$, if $\operatorname{MEX}([b_1, b_2, \dots, b_k]) = k$, then the array $b$ is called a $k$-good array.

Given a positive integer $n$, for an $n$-good array $p_1, p_2, \dots, p_n$, Little N defines the function $f(p)$ as the number of integer pairs $(l, r)$ that satisfy the following conditions:

• $1 \le l \le r \le n$;
• $p_l, \dots, p_r$ is a $(r - l + 1)$-good array.

Little N has proven the following theorem: for any $n$-good array $p$, there holds $1 \le f(p) \le n$. Now, Little N hopes you can find the number of $n$-good arrays $p$ for each $i \in [1, n]$ such that $f(p) = i$. Of course, this number may be very large, so you need to provide the result modulo $998\,244\,353$.

Input

The input consists of a single line containing an integer $n$ ($1 \le n \le 10^5$).

Output

Output a single line containing $n$ integers, where the $i$-th integer represents the number of $n$-good arrays $p$ satisfying $f(p) = i$, modulo $998\,244\,353$.

Examples

Sample Input 1

1

Sample Output 1

1

Sample Input 2

3

Sample Output 2

0 2 4

Sample Input 3

7

Sample Output 3

0 2312 1424 728 352 160 64

Note

For $n = 3$, it can be proven that there are six $3$-good arrays, with corresponding function values:

$f([0, 1, 2]) = 3$, $f([0, 2, 1]) = 2$, $f([1, 0, 2]) = 3$, $f([1, 2, 0]) = 2$, $f([2, 0, 1]) = 3$, $f([2, 1, 0]) = 3$