LR Constraints

AtCoder

IDarc124_a

Time2000ms

Memory256MB

Difficulty—

We have $N$ cards arranged in a row from left to right. We will write an integer between $1$ and $K$ (inclusive) on each of these cards, which are initially blank. Given are $K$ restrictions numbered $1$ through $K$. Restriction $i$ is composed of a character $c_i$ and an integer $k_i$. If $c_i$ is `L`, the $k_i$\-th card from the left in the row must be the **leftmost** card on which we write $i$. If $c_i$ is `R`, the $k_i$\-th card from the left in the row must be the **rightmost** card on which we write $i$. Note that for each integer $i$ from $1$ through $K$, there must be at least one card on which we write $i$. Find the number of ways to write integers on the cards under the $K$ restrictions, modulo $998244353$. ## Constraints * $1 \leq N,K \leq 1000$ * $c_i$ is `L` or `R`. * $1 \leq k_i \leq N$ * $k_i \neq k_j$ if $i \neq j$. ## Input Input is given from Standard Input in the following format: $N$ $K$ $c_1$ $k_1$ $\vdots$ $c_K$ $k_K$ [samples]

Samples

Input #1

3 2
L 1
R 2

Output #1

1

*   The only way to meet the two restrictions is to write $1, 2, 1$ from left to right on the three cards.

Input #2

Output #2

343921442

*   Be sure to find the count modulo $998244353$.

API Response (JSON)

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