P13012 【MX-X13-T7】"KDOI-12" No one can be anything without comparison.

**Please note the special constraints on $\bm{n,k}$ in this problem.** $n$ players participated in $k$ Tetris Tournaments. Each Tetris Tournament consists of $n-1$ rounds. In each round, two currently uneliminated players $x$ and $y$ are selected to compete, and the loser is eliminated. The last remaining player is the winner. You are given that the $j$-th player was eliminated by $a_{i,j}$ in the $i$-th Tetris Tournament. Here, $j$ is the winner of the $i$-th tournament if and only if $a_{i,j} = 0$. The players enjoy comparison. They all hope to surpass others in some way or at least be on a similar level. Define that in the $i$-th Tetris Tournament, $x$ **strictly dominates** $y$ if and only if there exists a sequence $x = p_1, p_2, \dots, p_m = y$ (where $m \ge 2$, i.e., $x \neq y$) such that for all $1 \leq j < m$, $a_{i,p_{j+1}} = p_j$. An ordered $k$-tuple of players $(i_1, i_2, \dots, i_k)$ is called **level-similar** if and only if for all $1 \leq j < k$, $i_j$ strictly dominates $i_{j+1}$ in the $j$-th tournament, and $i_k$ strictly dominates $i_1$ in the $k$-th tournament. Your task is to compute the number of level-similar $k$-tuples, modulo $998244353$.

The first line contains two positive integers $n$ and $k$. **It is guaranteed that $\bm{3 \leq k \leq 5}$.** The next $k$ lines each contain $n$ non-negative integers $a_{i,1}, \ldots, a_{i,n}$, representing the elimination data for the $i$-th tournament.

Output a single non-negative integer: the number of level-similar $k$-tuples, modulo $998244353$.

### Sample Explanation #1 The valid $3$-tuples $(i_1, i_2, i_3)$ are: $(1, 2, 3)$ and $(2, 3, 1)$. ### Constraints **This problem uses bundling tests.** | Subtask | Points | $n\leq$ | $k=$ | Special Constraints | |:--:|:--:|:--:|:--:|:--:| | $1$ | $7$ | $100$ | $3$ | None | | $2$ | $8$ | $500$ | $3$ | None | | $3$ | $13$ | $3\times10^3$ | $3$ | None | | $4$ | $14$ | $2.5\times10^5$ | $3$ | A | | $5$ | $15$ | $10^5$ | $3$ | B | | $6$ | $7$ | $10^5$ | $3$ | None | | $7$ | $14$ | $2.5\times10^5$ | $3$ | None | | $8$ | $7$ | $5\times10^4$ | $4$ | None | | $9$ | $6$ | $7.5\times10^4$ | $4$ | None | | $10$ | $9$ | $4\times10^4$ | $5$ | None | - **Special Constraint A**: For $1 \leq i \leq n$, $a_{1,i} = a_{2,i}$. - **Special Constraint B**: For $1 \leq i \leq k$, there do not exist $1 \leq j_1 < j_2 \leq n$ such that $a_{i,j_1} = a_{i,j_2}$. For all test cases: - $1 \leq n \leq 2.5 \times 10^5$, - $\bm{3 \leq k \leq 5}$, - The $a$ array is consistent with the problem description, and: - If $k=3$, $n \leq 2.5 \times 10^5$. - If $k=4$, $n \leq 7.5 \times 10^4$. - If $k=5$, $n \leq 4 \times 10^4$. --- *Translation by DeepSeek V3.*