Akari

AtCoder

IDabc182_e

Time2500ms

Memory256MB

Difficulty—

We have a grid with $H$ rows and $W$ columns. Let square $(i, j)$ be the square at the $i$\-th row and $j$\-th column in this grid. There are $N$ bulbs and $M$ blocks on this grid. The $i$\-th bulb is at square $(A_i, B_i)$, and the $i$\-th block is at square $(C_i, D_i)$. There is at most one object - a bulb or a block - at each square. Every bulb emits beams of light in four directions - up, down, left, and right - that extend until reaching a square with a block, illuminating the squares on the way. A square with a bulb is also considered to be illuminated. Among the squares without a block, find the number of squares illuminated by the bulbs. ## Constraints * $1 \le H, W \le 1500$ * $1 \le N \le 5 \times 10^5$ * $1 \le M \le 10^5$ * $1 \le A_i \le H$ * $1 \le B_i \le W$ * $1 \le C_i \le H$ * $1 \le D_i \le W$ * $(A_i, B_i) \neq (A_j, B_j)\ \ (i \neq j)$ * $(C_i, D_i) \neq (C_j, D_j)\ \ (i \neq j)$ * $(A_i, B_i) \neq (C_j, D_j)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $H$ $W$ $N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $A_3$ $B_3$ $\hspace{15pt} \vdots$ $A_N$ $B_N$ $C_1$ $D_1$ $C_2$ $D_2$ $C_3$ $D_3$ $\hspace{15pt} \vdots$ $C_M$ $D_M$ [samples]

Samples

Input #1

Output #1

7

Among the squares without a block, all but square $(3, 2)$ are illuminated.

Input #2

Output #2

8

Among the squares without a block, the following eight are illuminated:

*   Square $(1, 1)$
*   Square $(1, 2)$
*   Square $(1, 3)$
*   Square $(1, 4)$
*   Square $(2, 2)$
*   Square $(3, 3)$
*   Square $(3, 4)$
*   Square $(4, 4)$

Input #3

Output #3

24

In this case, all the squares without a block are illuminated.

API Response (JSON)

{
  "problem": {
    "name": "Akari",
    "description": {
      "content": "We have a grid with $H$ rows and $W$ columns. Let square $(i, j)$ be the square at the $i$\\-th row and $j$\\-th column in this grid.   There are $N$ bulbs and $M$ blocks on this grid. The $i$\\-th bulb ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2500,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc182_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a grid with $H$ rows and $W$ columns. Let square $(i, j)$ be the square at the $i$\\-th row and $j$\\-th column in this grid.  \nThere are $N$ bulbs and $M$ blocks on this grid. The $i$\\-th bulb ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments