Pyramid

AtCoder

IDabc112_c

Time3000ms

Memory256MB

Difficulty—

In the Ancient Kingdom of Snuke, there was a pyramid to strengthen the authority of Takahashi, the president of AtCoder Inc. The pyramid had _center coordinates_ $(C_X, C_Y)$ and _height_ $H$. The altitude of coordinates $(X, Y)$ is $max(H - |X - C_X| - |Y - C_Y|, 0)$. Aoki, an explorer, conducted a survey to identify the center coordinates and height of this pyramid. As a result, he obtained the following information: * $C_X, C_Y$ was integers between $0$ and $100$ (inclusive), and $H$ was an integer not less than $1$. * Additionally, he obtained $N$ pieces of information. The $i$\-th of them is: "the altitude of point $(x_i, y_i)$ is $h_i$." This was enough to identify the center coordinates and the height of the pyramid. Find these values with the clues above. ## Constraints * $N$ is an integer between $1$ and $100$ (inclusive). * $x_i$ and $y_i$ are integers between $0$ and $100$ (inclusive). * $h_i$ is an integer between $0$ and $10^9$ (inclusive). * The $N$ coordinates $(x_1, y_1), (x_2, y_2), (x_3, y_3), ..., (x_N, y_N)$ are all different. * The center coordinates and the height of the pyramid can be uniquely identified. ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $h_1$ $x_2$ $y_2$ $h_2$ $x_3$ $y_3$ $h_3$ $:$ $x_N$ $y_N$ $h_N$ [samples]

Samples

Input #1

Output #1

2 2 6

In this case, the center coordinates and the height can be identified as $(2, 2)$ and $6$.

Input #2

2
0 0 100
1 1 98

Output #2

0 0 100

In this case, the center coordinates and the height can be identified as $(0, 0)$ and $100$.  
Note that $C_X$ and $C_Y$ are known to be integers between $0$ and $100$.

Input #3

Output #3

100 0 193

In this case, the center coordinates and the height can be identified as $(100, 0)$ and $193$.

API Response (JSON)

{
  "problem": {
    "name": "Pyramid",
    "description": {
      "content": "In the Ancient Kingdom of Snuke, there was a pyramid to strengthen the authority of Takahashi, the president of AtCoder Inc.   The pyramid had _center coordinates_ $(C_X, C_Y)$ and _height_ $H$. The a",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc112_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In the Ancient Kingdom of Snuke, there was a pyramid to strengthen the authority of Takahashi, the president of AtCoder Inc.  \nThe pyramid had _center coordinates_ $(C_X, C_Y)$ and _height_ $H$. The a...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments