Problem J
We Need to Go Deeper
Steve, Alex, and Kai have finally collected enough obsidian to get to the Nether, but something is on Steve’s mind. The three have collected quite a lot of obsidian, and Steve has heard that nether portals must be made as an empty rectangular frame (including the corners for this problem) with width at least 4 and at most 23 and height at least 5 and at most 23.
Given the amount of obsidian the three have, how many different ways can a single nether portal be created (leftover obsidian is okay). For our purposes, we count both orientations as distinct as long as the portal is not square (so $5 \times 5$ is a unique configuration, but $5 \times 6$ is a distinct configuration from $6 \times 5$).
Input
The input contains a single integer, $x$, the amount of obsidian. You are given that $1 \le x \le 23^2$.
Output
Output a single integer, $y$, the number of distinct nether portal configurations that can be achieved.
| Sample Input 1 | Sample Output 1 |
|---|---|
14 |
1 |
| Sample Input 2 | Sample Output 2 |
|---|---|
13 |
0 |
| Sample Input 3 | Sample Output 3 |
|---|---|
35 |
66 |