Neq Neq

AtCoder

IDarc128_d

Time2000ms

Memory256MB

Difficulty—

We have $N$ balls arranged in a row, numbered $1$ to $N$ from left to right. Ball $i$ has an integer $A_i$ written on it. You can do the following operation any number of times. * Choose three consecutive balls $x, y, z$ $(1 \leq x < y < z \leq N$). Here, $A_x \neq A_y$ and $A_y \neq A_z$ must hold. Then, eat Ball $y$. After this operation, Balls $x$ and $z$ are considered adjacent. Find the number of possible sets of balls remaining in the end, modulo $998244353$. ## Constraints * $2 \leq N \leq 200000$ * $1 \leq A_i \leq N$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

4
1 2 1 2

Output #1

3

There are three possible sets of balls remaining in the end: ${1,2,3,4},{1,2,4},{1,3,4}$.

Input #2

5
5 4 3 2 1

Output #2

8

Different sequences of operations are not distinguished if they result in the same set of balls.

Input #3

5
1 2 3 2 1

Output #3

8

Different sets of remaining balls are distinguished even if they have the same sequence of integers written on them.

Input #4

9
1 4 2 2 9 6 9 6 6

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Neq Neq",
    "description": {
      "content": "We have $N$ balls arranged in a row, numbered $1$ to $N$ from left to right. Ball $i$ has an integer $A_i$ written on it. You can do the following operation any number of times. *   Choose three cons",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc128_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ balls arranged in a row, numbered $1$ to $N$ from left to right. Ball $i$ has an integer $A_i$ written on it.\nYou can do the following operation any number of times.\n\n*   Choose three cons...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments