Power Up

AtCoder

IDarc160_c

Time2000ms

Memory256MB

Difficulty—

You are given a multiset of positive integers with $N$ elements: $A=\lbrace A_1,A_2,\dots,A_N \rbrace$. You may repeat the following operation any number of times (possibly zero). * Choose a positive integer $x$ that occurs at least twice in $A$. Delete two occurrences of $x$ from $A$, and add one occurrence of $x+1$ to $A$. Find the number, modulo $998244353$, of multisets that $A$ can be in the end. ## Constraints * $1 \le N \le 2 \times 10^5$ * $1 \le A_i \le 2 \times 10^5$ ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

4
1 1 2 4

Output #1

3

$A$ can be one of the three multisets $\lbrace 1,1,2,4 \rbrace,\lbrace 2,2,4 \rbrace,\lbrace 3,4 \rbrace$ in the end.
You can make $A = \lbrace 3,4 \rbrace$ as follows.

*   Choose $x = 1$. Delete two $1$s from $A$ and add one $2$ to $A$, making $A=\lbrace 2,2,4 \rbrace$.
*   Choose $x = 2$. Delete two $2$s from $A$ and add one $3$ to $A$, making $A=\lbrace 3,4 \rbrace$.

Input #2

5
1 2 3 4 5

Output #2

Input #3

13
3 1 4 1 5 9 2 6 5 3 5 8 9

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Power Up",
    "description": {
      "content": "You are given a multiset of positive integers with $N$ elements: $A=\\lbrace A_1,A_2,\\dots,A_N \\rbrace$. You may repeat the following operation any number of times (possibly zero). *   Choose a positi",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc160_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a multiset of positive integers with $N$ elements: $A=\\lbrace A_1,A_2,\\dots,A_N \\rbrace$.\nYou may repeat the following operation any number of times (possibly zero).\n\n*   Choose a positi...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments