Flipper

AtCoder

IDagc051_c

Time2000ms

Memory256MB

Difficulty—

There is a square grid of dimensions $10^9 \times 10^9$. The cells are numbered $(1, 1)$ through $(10^9, 10^9)$. Cell $(i, j)$ is in the $i$\-th row from the top, and the $j$\-th column from the left. Initially, $N$ cells $(x_1, y_1), \ldots, (x_N, y_N)$ are black, and all other cells are white. Snuke can perform the following operation an arbitrary number of times: * Choose an integer $x (1 \leq x \leq 10^9 - 1)$ and an integer $y (1 \leq y \leq 10^9 - 2)$, and flip (black to white, white to black) the colors of the following six cells: $(x, y), (x, y+1), (x, y+2), (x+1, y), (x+1, y+1), (x+1, y+2)$ Compute the minimum possible number of black cells after the operations. ## Constraints * $1 \leq N \leq 10^5$ * $1 \leq x_i, y_i \leq 10^9$ * $(x_i, y_i)$ are pairwise distinct. * All values in the input are integers. ## Input Input is given from Standard Input in the following format: $N$ $x_1 \ y_1$ $:$ $x_N \ y_N$ [samples]

Samples

Input #1

Output #1

3

In the diagram below, the $j$\-th letter of the $i$\-th string from the top represents the cell $(i, j)$. `#` is black, `.` is white.

.##.
#.##
.###
.#..

->

#...
.#.#
.###
.#..

->

#...
..#.
....
.#..

API Response (JSON)

{
  "problem": {
    "name": "Flipper",
    "description": {
      "content": "There is a square grid of dimensions $10^9 \\times 10^9$. The cells are numbered $(1, 1)$ through $(10^9, 10^9)$. Cell $(i, j)$ is in the $i$\\-th row from the top, and the $j$\\-th column from the left.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc051_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a square grid of dimensions $10^9 \\times 10^9$. The cells are numbered $(1, 1)$ through $(10^9, 10^9)$. Cell $(i, j)$ is in the $i$\\-th row from the top, and the $j$\\-th column from the left....",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments