A13666. Omkar and Last Class of Math

In Omkar's last class of math, he learned about the least common multiple, or $LCM$ . $LCM(a, b)$ is the smallest positive integer $x$ which is divisible by both $a$ and $b$ .

Omkar, having a laudably curious mind, immediately thought of a problem involving the $LCM$ operation: given an integer $n$ , find positive integers $a$ and $b$ such that $a + b = n$ and $LCM(a, b)$ is the minimum value possible.

Can you help Omkar solve his ludicrously challenging math problem?

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \leq t \leq 10$ ). Description of the test cases follows.

Each test case consists of a single integer $n$ ( $2 \leq n \leq 10^{9}$ ).

For each test case, output two positive integers $a$ and $b$ , such that $a + b = n$ and $LCM(a, b)$ is the minimum possible.

For the first test case, the numbers we can choose are $1, 3$ or $2, 2$ . $LCM(1, 3) = 3$ and $LCM(2, 2) = 2$ , so we output $2 \ 2$ .

For the second test case, the numbers we can choose are $1, 5$ , $2, 4$ , or $3, 3$ . $LCM(1, 5) = 5$ , $LCM(2, 4) = 4$ , and $LCM(3, 3) = 3$ , so we output $3 \ 3$ .

For the third test case, $LCM(3, 6) = 6$ . It can be shown that there are no other pairs of numbers which sum to $9$ that have a lower $LCM$ .