Not Argmax

AtCoder

IDarc183_c

Time2000ms

Memory256MB

Difficulty—

Find the number, modulo $998244353$, of permutations $P=(P_1,P_2,\cdots,P_N)$ of $(1,2,\cdots,N)$ that satisfy all of the following $M$ conditions. * The $i$\-th condition: The maximum among $P_{L_i},P_{L_i+1},\cdots,P_{R_i}$ is **not** $P_{X_i}$. Here, $L_i$, $R_i$, and $X_i$ are integers given in the input. ## Constraints * $1 \leq N \leq 500$ * $1 \leq M \leq 10^5$ * $1 \leq L_i \leq X_i \leq R_i \leq N$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $L_1$ $R_1$ $X_1$ $L_2$ $R_2$ $X_2$ $\vdots$ $L_M$ $R_M$ $X_M$ [samples]

Samples

Input #1

3 2
1 3 2
1 2 1

Output #1

1

Only one permutation, $P=(1,2,3)$, satisfies the conditions.

Input #2

5 1
1 1 1

Output #2

Input #3

Output #3

Input #4

Output #4

921467228

API Response (JSON)

{
  "problem": {
    "name": "Not Argmax",
    "description": {
      "content": "Find the number, modulo $998244353$, of permutations $P=(P_1,P_2,\\cdots,P_N)$ of $(1,2,\\cdots,N)$ that satisfy all of the following $M$ conditions. *   The $i$\\-th condition: The maximum among $P_{L_",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc183_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Find the number, modulo $998244353$, of permutations $P=(P_1,P_2,\\cdots,P_N)$ of $(1,2,\\cdots,N)$ that satisfy all of the following $M$ conditions.\n\n*   The $i$\\-th condition: The maximum among $P_{L_...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments