Min-Max of Three Numbers

Problem Description

Given a positive integer $n$. Among all triples of three distinct positive integers that sum to $n$, find:

• $x$: the smallest possible value of the largest of the three numbers;
• $y$: the largest possible value of the smallest of the three numbers.

For example, when $n = 10$, choosing $2, 3, 5$ makes the largest number as small as $5$, and the smallest number as large as $2$.

Input Format

A single positive integer $n$ ($0 < n < 10000$).

Output Format

Output two positive integers $x$ and $y$, separated by a single space. If no such triple exists, output -1 -1.

Sample Input 1

3

Sample Output 1

-1 -1

Sample Input 2

6

Sample Output 2

3 1

Sample Input 3

17

Sample Output 3

7 4

Hint

1. Note that they are $3$ distinct positive integers.
2. The programming approach may differ from the mathematical reasoning in the statement; you can also find the answer directly by enumerating with loops.