Description

This is a pattern-finding problem. Please discover the pattern yourself to practice mathematical induction!!

Let’s take triangular numbers as an example: the numbers $1$, $3$, $6$, $10$ in the figure are triangular numbers.

Task: determine which kinds of polygonal numbers $N$ belongs to (assume $N$ is a $K$-gonal number). For example, we can find that $36$ is both a triangular number and a square number. If it is not a polygonal number, output Poor + that number. If it is multiple types of polygonal numbers at the same time, output the smallest $K$ and the second smallest $K$. Each input file contains $ng$ test cases.

Input Format

First a number $ng$, then $ng$ lines, each containing one integer.

Output Format

Output $ng$ lines. For each $N$, output the corresponding $K_1$ and $K_2$. If $N$ is not a polygonal number, output Poor + that number (no spaces in between).

2
36
1000000

3 4
4 204

Hint

Constraints and Notes

For $20\%$ of the testdata, $1 \le K_1, K_2 \le 6$.

For $100\%$ of the testdata, $1 \le N \le 10^6$, $1 \le ng \le 10^2$.

If $N$ is multiple types of polygonal numbers at the same time, let $K_1$ be the smallest $K$, and $K_2$ be the second smallest $K$.

King $1$: "Can you discover the pattern that square numbers are just perfect squares? To make it easier to understand, I’ll provide a table of the first few polygonal numbers." (From the table you can see that a regular hexagon does not include the very center point, and similarly for others.)

Translated by ChatGPT 5