Crush

There are $N$ students in Seondeok High School. The students are numbered $1,2,\cdots,N$ without duplication.

Each student has a crush on exactly one other student, not themselves. The teacher knows this information only for some students; for the remaining students, the teacher does not know whom they have a crush on.

When all unknown information is completed, the teacher wants to know the number of possible completions such that exactly $K$ pairs of students like each other. A pair of students liking each other means that two distinct students $i,j$ satisfy that $i$ has a crush on $j$ and $j$ has a crush on $i$.

For each test case, compute the answer for every $K=0,1,2,\cdots,N-1$. Since the number of possible completions can be large, print each answer modulo $998\ 244\ 353$.

The input is given in the following format.

$T$ $N$ $B_1\ B_2\ \cdots\ B_N$ $N$ $B_1\ B_2\ \cdots\ B_N$ $\vdots$

For each test case, $B_i$ represents the information about student $i$. If $B_i=-1$, then it is unknown whom student $i$ has a crush on. If $B_i \neq -1$, then student $i$ has a crush on student $B_i$.

For each test case, print $N$ integers on one line, separated by spaces.

The $i$-th integer must be the number of possible completions when $K=i-1$, modulo $998\ 244\ 353$.

• $1 \leq T \leq 1\ 000$.
• $2 \leq N \leq 200\ 000$.
• The sum of $N$ over all test cases is at most $200\ 000$.
• $B_i=-1$ or $1 \leq B_i \leq N$ ($1 \leq i \leq N$).
• $B_i \neq i$ ($1 \leq i \leq N$), except when $B_i=-1$.