P5086 Coordinates

Solution write-up: . Xiaoben knows that Minecraft coordinates have three parameters: $X$, $Y$, and $Z$. But in Xiaoben’s eyes, there is a fourth parameter $Q$, which represents how much he likes this location. For example, some places are Xiaoben’s home, so $Q$ will be large; some places are dangerous mines, so $Q$ will be small.

There are $N$ coordinates. For the $i$-th coordinate with parameters $\{X _ i, Y _ i, Z _ i, Q _ i\}$ and the $j$-th coordinate with parameters $\{X _ j, Y _ j, Z _ j, Q _ j\}$, if $X _ i - X _ j = Y _ i - Y _ j = Z _ i - Z _ j = Q _ i - Q _ j$, then these coordinates are called beautiful coordinates. Given $N$ coordinates, Xiaoben wants to know the minimum value of $j - i$ and the maximum value of $i + j$ among all beautiful coordinate pairs. Can you help him?

The input has $n + 1$ lines. The first line contains an integer $n$. Then follow $n$ lines, each containing four integers $X$, $Y$, $Z$, and $Q$.

Output one line containing the minimum value of $j - i$ and the maximum value of $i + j$, separated by a space. The testdata guarantees that a solution exists.

### Explanation for Sample 1 $(1, 2, 3, 4)$ and $(2, 3, 4, 5)$, or $(1, 4, 3, 3)$ and $(2, 5, 4, 4)$, achieve the minimum value. For $(1, 4, 3, 3)$ and $(2, 5, 4, 4)$, $6 + 7 = 13$ is the maximum value. ### Constraints For $30\%$ of the data, $n \le 10 ^ 3$. For $100\%$ of the data, $1 \le n \le 5 \times 10 ^ 5$, and $X$, $Y$, $Z$, $Q$ are all within the `int` range. Translated by ChatGPT 5