Colorful Hats 2

AtCoder

IDsumitb2019_e

Time2000ms

Memory256MB

Difficulty—

$N$ people are standing in a queue, numbered $1, 2, 3, ..., N$ from front to back. Each person wears a hat, which is red, blue, or green. The person numbered $i$ says: * "In front of me, exactly $A_i$ people are wearing hats with the same color as mine." Assuming that all these statements are correct, find the number of possible combinations of colors of the $N$ people's hats. Since the count can be enormous, compute it modulo $1000000007$. ## Constraints * $1 \leq N \leq 100000$ * $0 \leq A_i \leq N-1$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $A_3$ $...$ $A_N$ [samples]

Samples

Input #1

6
0 1 2 3 4 5

Output #1

3

We have three possible combinations, as follows:

*   Red, Red, Red, Red, Red, Red
*   Blue, Blue, Blue, Blue, Blue, Blue
*   Green, Green, Green, Green, Green, Green

Input #2

3
0 0 0

Output #2

Input #3

54
0 0 1 0 1 2 1 2 3 2 3 3 4 4 5 4 6 5 7 8 5 6 6 7 7 8 8 9 9 10 10 11 9 12 10 13 14 11 11 12 12 13 13 14 14 15 15 15 16 16 16 17 17 17

Output #3

115295190

API Response (JSON)

{
  "problem": {
    "name": "Colorful Hats 2",
    "description": {
      "content": "$N$ people are standing in a queue, numbered $1, 2, 3, ..., N$ from front to back. Each person wears a hat, which is red, blue, or green. The person numbered $i$ says: *   \"In front of me, exactly $A",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "sumitb2019_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$N$ people are standing in a queue, numbered $1, 2, 3, ..., N$ from front to back. Each person wears a hat, which is red, blue, or green.\nThe person numbered $i$ says:\n\n*   \"In front of me, exactly $A...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments