Good Division

AtCoder

IDarc159_f

Time5000ms

Memory256MB

Difficulty—

A sequence $X$ is called **good** when the following holds. * $X$ can be emptied by repeating the following operation zero or more times. * Delete two adjacent elements $x_i$ and $x_{i+1}$ of $X$ such that $x_i \neq x_{i+1}$. You are given a sequence with $2N$ elements: $A=(a_1,\ldots,a_{2N})$. Among the $2^{2N-1}$ ways to divide $A$ into one or more contiguous subsequences, how many are such that all those contiguous subsequences are good? Find the count modulo $998244353$. ## Constraints * $1 \leq N \leq 5 \times 10^5$ * $1 \leq a_i \leq 2N$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $a_1$ $\ldots$ $a_{2N}$ [samples]

Samples

Input #1

3
1 1 2 3 4 5

Output #1

2

The following two divisions satisfy the condition.

*   $(1,1,2,3,4,5)$
*   $(1,1,2,3),(4,5)$

Input #2

1
1 2

Output #2

Input #3

1
1 1

Output #3

Input #4

12
4 2 17 12 18 15 17 4 22 6 9 20 21 16 23 16 13 2 20 15 16 3 7 15

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Good Division",
    "description": {
      "content": "A sequence $X$ is called **good** when the following holds. *   $X$ can be emptied by repeating the following operation zero or more times.     *   Delete two adjacent elements $x_i$ and $x_{i+1}$ of",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc159_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "A sequence $X$ is called **good** when the following holds.\n\n*   $X$ can be emptied by repeating the following operation zero or more times.\n    *   Delete two adjacent elements $x_i$ and $x_{i+1}$ of...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments