P15764 [JAG 2025 Summer Camp #1] LOGCFL

You are given a 3-dimensional integer array $A$ of size $N \times N \times N$. Initialize the following variables: ``` integer x = 0; integer w = 1; stack s = {}; ``` Then, for each $t = 0, 1, \ldots, N - 1$, choose an integer $y_t$ such that $-1 \leq y_t < N$ and do the following action: If $0 \leq y_t$, do the following: ``` w *= A[t][x][y]; s.push(x); x = y; ``` The above $y$ denotes $y_t$. If $y_t = -1$, do the following: ``` assert (!s.empty()); w *= A[t][x][s.top()]; x = (x + s.top()) % N; s.pop(); ``` You can't choose $y_t = -1$ if the stack is empty before the action. Note that the stack has the following operations: - **push(x)**: adds an element $x$ to the collection. - **pop()**: removes the most recently added element. - **top()**: returns the value of the most recently added element. For each $i = 0, 1, \ldots, N - 1$, consider all possible sequences $y_0, y_1, \ldots, y_{N-1}$ such that the final value of $x$ is $i$. Compute the sum of the corresponding values of $w$ over all such sequences, and output the result modulo $998244353$.

The input is given in the following format: $$\begin{aligned} & N \\ & A_{0,0,0} \cdots A_{0,0,N-1} \\ & \vdots \\ & A_{0,N-1,0} \cdots A_{0,N-1,N-1} \\ & \vdots \\ & \vdots \\ & A_{N-1,0,0} \cdots A_{N-1,0,N-1} \\ & \vdots \\ & A_{N-1,N-1,0} \cdots A_{N-1,N-1,N-1} \end{aligned}$$ $A_{i,j,k}$ means the value of $A[i][j][k]$. - $1 \leq N \leq 30$ - $0 \leq A_{i,j,k} \leq 10^9 \ (1 \leq i, j, k \leq N)$ - All input values are integers.

Output $N$ lines. On the $i$-th line ($0 \leq i < N$), output the answer for $i$.