10517: ABC112 —— C - Pyramid
[Creator : ]
Description
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.
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.
Input
Input is given from Standard Input in the following format:
```
$N$
$x_1$ $y_1$ $h_1$
$x_2$ $y_2$ $h_2$
$x_3$ $y_3$ $h_3$
$:$
$x_N$ $y_N$ $h_N$
```
```
$N$
$x_1$ $y_1$ $h_1$
$x_2$ $y_2$ $h_2$
$x_3$ $y_3$ $h_3$
$:$
$x_N$ $y_N$ $h_N$
```
Output
Print values $C_X, C_Y$ and $H$ representing the center coordinates and the height of the pyramid in one line, with spaces in between.
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.
- $x_i$ 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.
Sample 1 Input
4
2 3 5
2 1 5
1 2 5
3 2 5
Sample 1 Output
2 2 6
In this case, the center coordinates and the height can be identified as (2,2) and 6.
Sample 2 Input
2
0 0 100
1 1 98
Sample 2 Output
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.
Sample 3 Input
3
99 1 191
100 1 192
99 0 192
Sample 3 Output
100 0 193
In this case, the center coordinates and the height can be identified as (100,0) and 193.