Cross Explosion

AtCoder

IDabc370_d

Time4000ms

Memory256MB

Difficulty—

There is a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the cell at the $i$\-th row from the top and $j$\-th column from the left. Initially, there is one wall in each cell. After processing $Q$ queries explained below in the order they are given, find the number of remaining walls. In the $q$\-th query, you are given two integers $R_q$ and $C_q$. You place a bomb at $(R_q, C_q)$ to destroy walls. As a result, the following process occurs. * If there is a wall at $(R_q, C_q)$, destroy that wall and end the process. * If there is no wall at $(R_q, C_q)$, destroy the first walls that appear when looking up, down, left, and right from $(R_q, C_q)$. More precisely, the following four processes occur simultaneously: * If there exists an $i \lt R_q$ such that a wall exists at $(i, C_q)$ and no wall exists at $(k, C_q)$ for all $i \lt k \lt R_q$, destroy the wall at $(i, C_q)$. * If there exists an $i \gt R_q$ such that a wall exists at $(i, C_q)$ and no wall exists at $(k, C_q)$ for all $R_q \lt k \lt i$, destroy the wall at $(i, C_q)$. * If there exists a $j \lt C_q$ such that a wall exists at $(R_q, j)$ and no wall exists at $(R_q, k)$ for all $j \lt k \lt C_q$, destroy the wall at $(R_q, j)$. * If there exists a $j \gt C_q$ such that a wall exists at $(R_q, j)$ and no wall exists at $(R_q, k)$ for all $C_q \lt k \lt j$, destroy the wall at $(R_q, j)$. ## Constraints * $1 \leq H, W$ * $H \times W \leq 4 \times 10^5$ * $1 \leq Q \leq 2 \times 10^5$ * $1 \leq R_q \leq H$ * $1 \leq C_q \leq W$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $H$ $W$ $Q$ $R_1$ $C_1$ $R_2$ $C_2$ $\vdots$ $R_Q$ $C_Q$ [samples]

Samples

Input #1

Output #1

2

The process of handling the queries can be explained as follows:

*   In the 1st query, $(R_1, C_1) = (1, 2)$. There is a wall at $(1, 2)$, so the wall at $(1, 2)$ is destroyed.
*   In the 2nd query, $(R_2, C_2) = (1, 2)$. There is no wall at $(1, 2)$, so the walls at $(2,2),(1,1),(1,3)$, which are the first walls that appear when looking up, down, left, and right from $(1, 2)$, are destroyed.
*   In the 3rd query, $(R_3, C_3) = (1, 3)$. There is no wall at $(1, 3)$, so the walls at $(2,3),(1,4)$, which are the first walls that appear when looking up, down, left, and right from $(1, 3)$, are destroyed.

After processing all queries, there are two remaining walls, at $(2, 1)$ and $(2, 4)$.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Cross Explosion",
    "description": {
      "content": "There is a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the cell at the $i$\\-th row from the top and $j$\\-th column from the left.   Initially, there is one wall in each cell.   After proce",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc370_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the cell at the $i$\\-th row from the top and $j$\\-th column from the left.  \nInitially, there is one wall in each cell.  \nAfter proce...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments