RGB Sequence

AtCoder

IDarc074_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ squares arranged in a row. The squares are numbered $1$, $2$, $...$, $N$, from left to right. Snuke is painting each square in red, green or blue. According to his aesthetic sense, the following $M$ conditions must all be satisfied. The $i$\-th condition is: * There are exactly $x_i$ different colors among squares $l_i$, $l_i + 1$, $...$, $r_i$. In how many ways can the squares be painted to satisfy all the conditions? Find the count modulo $10^9+7$. ## Constraints * $1 ≤ N ≤ 300$ * $1 ≤ M ≤ 300$ * $1 ≤ l_i ≤ r_i ≤ N$ * $1 ≤ x_i ≤ 3$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $l_1$ $r_1$ $x_1$ $l_2$ $r_2$ $x_2$ $:$ $l_M$ $r_M$ $x_M$ [samples]

Samples

Input #1

3 1
1 3 3

Output #1

6

The six ways are:

*   RGB
*   RBG
*   GRB
*   GBR
*   BRG
*   BGR

where R, G and B correspond to red, green and blue squares, respectively.

Input #2

4 2
1 3 1
2 4 2

Output #2

6

The six ways are:

*   RRRG
*   RRRB
*   GGGR
*   GGGB
*   BBBR
*   BBBG

Input #3

Output #3

0

There are zero ways.

Input #4

Output #4

API Response (JSON)

{
  "problem": {
    "name": "RGB Sequence",
    "description": {
      "content": "There are $N$ squares arranged in a row. The squares are numbered $1$, $2$, $...$, $N$, from left to right. Snuke is painting each square in red, green or blue. According to his aesthetic sense, the f",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc074_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ squares arranged in a row. The squares are numbered $1$, $2$, $...$, $N$, from left to right.\nSnuke is painting each square in red, green or blue. According to his aesthetic sense, the f...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments