Colorful Lines

AtCoder

IDarc130_b

Time2000ms

Memory256MB

Difficulty—

We have an $H\times W$ grid. Initially, the squares are unpainted. You will paint these squares. There are $C$ colors available, numbered $1, 2, \ldots, C$. The painting process will be given as $Q$ queries. The $i$\-th query contains integers $t_i, n_i, c_i$, which represents the following action. * If $t_i = 1$: paint all squares in the $n_i$\-th **row** with Color $c_i$. * If $t_i = 2$: paint all squares in the $n_i$\-th **column** with Color $c_i$. Painting a square with Color $c$ makes the color of that square Color $c$, regardless of its previous state. Find the number of squares painted in each of Color $1, 2, \ldots, C$ after the whole process. ## Constraints * $2\leq H\leq 10^9$ * $2\leq W\leq 10^9$ * $1\leq C\leq 3\times 10^5$ * $1\leq Q\leq 3\times 10^5$ * $t_i\in {1,2}$ * $1\leq n_i\leq H$ if $t_i = 1$ * $1\leq n_i\leq W$ if $t_i = 2$ * $1\leq c_i\leq C$ ## Input Input is given from Standard Input in the following format: $H$ $W$ $C$ $Q$ $t_1$ $n_1$ $c_1$ $\vdots$ $t_Q$ $n_Q$ $c_Q$ [samples]

Samples

Input #1

Output #1

0 8 3 3 0 0

The process changes the colors of the squares as follows. Here, `.` denotes an unpainted square.

.....   66666   66666   64666   64626   22222
.....   .....   .....   .4...   .4.2.   .4.2.
.....   .....   33333   34333   34323   34323
.....   .....   .....   .4...   .4.2.   .4.2.

Input #2

1000000000 1000000000 3 5
1 1 2
1 2 2
1 3 2
1 4 2
1 5 2

Output #2

0 5000000000 0

API Response (JSON)

{
  "problem": {
    "name": "Colorful Lines",
    "description": {
      "content": "We have an $H\\times W$ grid. Initially, the squares are unpainted. You will paint these squares. There are $C$ colors available, numbered $1, 2, \\ldots, C$. The painting process will be given as $Q$ q",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc130_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have an $H\\times W$ grid. Initially, the squares are unpainted.\nYou will paint these squares. There are $C$ colors available, numbered $1, 2, \\ldots, C$.\nThe painting process will be given as $Q$ q...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments