Adjacent Chmax

AtCoder

IDagc058_b

Time2000ms

Memory256MB

Difficulty—

You are given a permutation $P=(P_1,P_2,\cdots,P_N)$ of $(1,2,\cdots,N)$. You may perform the following operation zero or more times. * Choose an integer $i$ ($1 \leq i \leq N-1$). Let $v=\max(P_i,P_{i+1})$ and replace the values of $P_i$ and $P_{i+1}$ with $v$. How many sequences are there that $P$ can be after your operations? Find the count modulo $998244353$. ## Constraints * $2 \leq N \leq 5000$ * $(P_1,P_2,\cdots,P_N)$ is a permutation of $(1,2,\cdots,N)$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $P_1$ $P_2$ $\cdots$ $P_N$ [samples]

Samples

Input #1

3
1 3 2

Output #1

4

The four sequences that $P$ can become are $(1,3,2)$, $(3,3,2)$, $(1,3,3)$, and $(3,3,3)$.

Input #2

4
2 1 3 4

Output #2

Input #3

10
4 9 6 3 8 10 1 2 7 5

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Adjacent Chmax",
    "description": {
      "content": "You are given a permutation $P=(P_1,P_2,\\cdots,P_N)$ of $(1,2,\\cdots,N)$. You may perform the following operation zero or more times. *   Choose an integer $i$ ($1 \\leq i \\leq N-1$). Let $v=\\max(P_i,",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc058_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a permutation $P=(P_1,P_2,\\cdots,P_N)$ of $(1,2,\\cdots,N)$.\nYou may perform the following operation zero or more times.\n\n*   Choose an integer $i$ ($1 \\leq i \\leq N-1$). Let $v=\\max(P_i,...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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