Hop Sugoroku

AtCoder

IDabc335_f

Time2500ms

Memory256MB

Difficulty—

There is a row of $N$ squares labeled $1,2,\dots,N$ and a sequence $A=(A_1,A_2,\dots,A_N)$ of length $N$. Initially, square $1$ is painted black, the other $N-1$ squares are painted white, and a piece is placed on square $1$. You may repeat the following operation any number of times, possibly zero: * When the piece is on square $i$, choose a positive integer $x$ and move the piece to square $i + A_i \times x$. * Here, you cannot make a move with $i + A_i \times x > N$. * Then, paint the square $i + A_i \times x$ black. Find the number of possible sets of squares that can be painted black at the end of the operations, modulo $998244353$. ## Constraints * All input values are integers. * $1 \le N \le 2 \times 10^5$ * $1 \le A_i \le 2 \times 10^5$ ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

5
1 2 3 1 1

Output #1

8

There are eight possible sets of squares painted black:

*   Square $1$
*   Squares $1,2$
*   Squares $1,2,4$
*   Squares $1,2,4,5$
*   Squares $1,3$
*   Squares $1,4$
*   Squares $1,4,5$
*   Squares $1,5$

Input #2

1
200000

Output #2

Input #3

40
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Output #3

721419738

Be sure to find the number modulo $998244353$.

API Response (JSON)

{
  "problem": {
    "name": "Hop Sugoroku",
    "description": {
      "content": "There is a row of $N$ squares labeled $1,2,\\dots,N$ and a sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$.   Initially, square $1$ is painted black, the other $N-1$ squares are painted white, and a pie",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2500,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc335_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a row of $N$ squares labeled $1,2,\\dots,N$ and a sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$.  \nInitially, square $1$ is painted black, the other $N-1$ squares are painted white, and a pie...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments