Problem Statement

You are given a prime $P$ and integer sequences $A_1,A_2,\dots,A_{P-1}$ and $B_1,B_2,\dots,B_{P-1}$.
Find the integer sequence $C_1,C_2,\dots,C_{P-1}$.
Here,
\[
C_k=\sum_{1 \le i,j \lt P\\ k=(i\times j) \mod P}A_iB_j
\]
and you should output these values modulo $998244353$.
(That is, $C_k$ is the sum of $A_iB_j$ over all pairs $(i,j)$ such that the remainder of $i\times j$ divided by $P$ is $k$.)

Constraints

Input

$P$
$A_1\ A_2\ \dots\ A_{P-1}$
$B_1\ B_2\ \dots\ B_{P-1}$

Output

Output $C_1,C_2,\dots,C_{P-1}$ modulo $998244353$, separated by spaces.
Print a newline at the end.

Sample

3
1 2
3 4

11 10

11
2 3 5 8 1 3 2 1 3 4
5 5 8 9 1 4 4 2 3 3

172 129 138 127 162 138 149 148 129 116

2
8886
112339

1