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D - Happy New Year 2023

Score : $400$ points

Problem Statement

You are given a positive integer $N$. It is known that $N$ can be represented as $N=p^2q$ using two different prime numbers $p$ and $q$.

Find $p$ and $q$.

You have $T$ test cases to solve.

Constraints

• All values in the input are integers.
• $1\leq T\leq 10$
• $1\leq N \leq 9\times 10^{18}$
• $N$ can be represented as $N=p^2q$ using two different prime numbers $p$ and $q$.

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Input

The input is given from Standard Input in the following format, where $\text{test}_i$ represents the $i$-th test case:

$T$

$\text{test}_1$

$\text{test}_2$

$\vdots$

$\text{test}_T$

Each test case is in the following format:

``` $N$ ```

Output

Print $T$ lines.

The $i$-th $(1\leq i \leq T)$ line should contain $p$ and $q$ for the $i$-th test case, separated by a space. Under the constraints of this problem, it can be proved that the pair of prime numbers $p$ and $q$ such that $N=p^2q$ is unique.

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3
2023
63
1059872604593911

17 7
3 7
104149 97711

For the first test case, we have $N=2023=17^2\times 7$. Thus, $p=17$ and $q=7$.