CF1372B 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 $ .