Paint

AtCoder

IDabc346_e

Time2000ms

Memory256MB

Difficulty—

There is a grid with $H$ rows and $W$ columns. Initially, all cells are painted with color $0$. You will perform the following operations in the order $i = 1, 2, \ldots, M$. * If $T_i = 1$, repaint all cells in the $A_i$\-th **row** with color $X_i$. * If $T_i = 2$, repaint all cells in the $A_i$\-th **column** with color $X_i$. After all operations are completed, for each color $i$ that exists on the grid, find the number of cells that are painted with color $i$. ## Constraints * $1 \leq H, W, M \leq 2 \times 10^5$ * $T_i \in \lbrace 1, 2 \rbrace$ * $1 \leq A_i \leq H$ for each $i$ such that $T_i = 1$, * $1 \leq A_i \leq W$ for each $i$ such that $T_i = 2$. * $0 \leq X_i \leq 2 \times 10^5$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $H$ $W$ $M$ $T_1$ $A_1$ $X_1$ $T_2$ $A_2$ $X_2$ $\vdots$ $T_M$ $A_M$ $X_M$ [samples]

Samples

Input #1

Output #1

3
0 5
2 4
5 3

The operations will change the colors of the cells in the grid as follows:

0000   0000   0000   0000   0000
0000 → 5555 → 5550 → 5550 → 5550 
0000   0000   0000   3333   2222

Eventually, there are five cells painted with color $0$, four with color $2$, and three with color $5$.

Input #2

Output #2

1
10000 1

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Paint",
    "description": {
      "content": "There is a grid with $H$ rows and $W$ columns. Initially, all cells are painted with color $0$. You will perform the following operations in the order $i = 1, 2, \\ldots, M$. *   If $T_i = 1$, repaint",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc346_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a grid with $H$ rows and $W$ columns. Initially, all cells are painted with color $0$.\nYou will perform the following operations in the order $i = 1, 2, \\ldots, M$.\n\n*   If $T_i = 1$, repaint...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments