Defect-free Squares

AtCoder

IDabc311_e

Time2000ms

Memory256MB

Difficulty—

There is a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the square at the $i$\-th row from the top and $j$\-th column from the left of the grid. Each square of the grid is holed or not. There are exactly $N$ holed squares: $(a_1, b_1), (a_2, b_2), \dots, (a_N, b_N)$. When the triple of positive integers $(i, j, n)$ satisfies the following condition, the square region whose top-left corner is $(i, j)$ and whose bottom-right corner is $(i + n - 1, j + n - 1)$ is called a **holeless square**. * $i + n - 1 \leq H$. * $j + n - 1 \leq W$. * For every pair of non-negative integers $(k, l)$ such that $0 \leq k \leq n - 1, 0 \leq l \leq n - 1$, square $(i + k, j + l)$ is not holed. How many holeless squares are in the grid? ## Constraints * $1 \leq H, W \leq 3000$ * $0 \leq N \leq \min(H \times W, 10^5)$ * $1 \leq a_i \leq H$ * $1 \leq b_i \leq W$ * All $(a_i, b_i)$ are pairwise different. * All input values are integers. ## Input The input is given from Standard Input in the following format: $H$ $W$ $N$ $a_1$ $b_1$ $a_2$ $b_2$ $\vdots$ $a_N$ $b_N$ [samples]

Samples

Input #1

2 3 1
2 3

Output #1

6

There are six holeless squares, listed below. For the first five, $n = 1$, and the top-left and bottom-right corners are the same square.

*   The square region whose top-left and bottom-right corners are $(1, 1)$.
*   The square region whose top-left and bottom-right corners are $(1, 2)$.
*   The square region whose top-left and bottom-right corners are $(1, 3)$.
*   The square region whose top-left and bottom-right corners are $(2, 1)$.
*   The square region whose top-left and bottom-right corners are $(2, 2)$.
*   The square region whose top-left corner is $(1, 1)$ and whose bottom-right corner is $(2, 2)$.

Input #2

Output #2

0

There may be no holeless square.

Input #3

1 1 0

Output #3

1

The whole grid may be a holeless square.

Input #4

3000 3000 0

Output #4

9004500500

API Response (JSON)

{
  "problem": {
    "name": "Defect-free Squares",
    "description": {
      "content": "There is a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left of the grid.   Each square of the grid is holed or not. T",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc311_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a grid with $H$ rows and $W$ columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left of the grid.  \nEach square of the grid is holed or not. T...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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