C - Pyramid

Score: $300$ points

Problem Statement

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:

$N$

$x_1$ $y_1$ $h_1$

$x_2$ $y_2$ $h_2$

$x_3$ $y_3$ $h_3$

$:$

$x_N$ $y_N$ $h_N$

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.

4
2 3 5
2 1 5
1 2 5
3 2 5

2 2 6

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

2
0 0 100
1 1 98

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 $100$.

3
99 1 191
100 1 192
99 0 192

100 0 193

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