Range Argmax

AtCoder

IDagc056_b

Time2000ms

Memory256MB

Difficulty—

Given are an integer $N$ and $M$ pairs of integers. The $i$\-th pair is $(L_i,R_i)$. Find the number of integer sequences $x=(x_1,x_2,\cdots,x_M)$ that can be generated as follows, modulo $998244353$. * Provide a permutation $p=(p_1,p_2,\cdots,p_N)$ of $(1,2,\cdots,N)$. * For each $i$ ($1 \leq i \leq M$), let $x_i$ be the index of the largest element among $p_{L_i},p_{L_i+1},\cdots,p_{R_i}$. That is, $\max(p_{L_i},p_{L_i+1},\cdots,p_{R_i})=p_{x_i}$. ## Constraints * $2 \leq N \leq 300$ * $1 \leq M \leq N(N-1)/2$ * $1 \leq L_i < R_i \leq N$ * $(L_i,R_i) \neq (L_j,R_j)$ ($i \neq j$) * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $L_1$ $R_1$ $L_2$ $R_2$ $\vdots$ $L_M$ $R_M$ [samples]

Samples

Input #1

3 2
1 2
1 3

Output #1

4

For example, for $p=(2,1,3)$, we will have $x=(1,3)$.
The four sequences that meet the requirement are $x=(1,1),(1,3),(2,2),(2,3)$.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Range Argmax",
    "description": {
      "content": "Given are an integer $N$ and $M$ pairs of integers. The $i$\\-th pair is $(L_i,R_i)$. Find the number of integer sequences $x=(x_1,x_2,\\cdots,x_M)$ that can be generated as follows, modulo $998244353$.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc056_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are an integer $N$ and $M$ pairs of integers. The $i$\\-th pair is $(L_i,R_i)$.\nFind the number of integer sequences $x=(x_1,x_2,\\cdots,x_M)$ that can be generated as follows, modulo $998244353$....",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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