Omkar and Last Class of Math

题意翻译

给出 $n$,输出 $a$ ,$b$ ($0 < a \leq b < n$),使$a+b=n$且 $\operatorname{lcm}(a,b)$ 最小。

题目描述

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?

输入输出格式

输入格式

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} $ ).

输出格式

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

输入输出样例

输入样例 #1

3
4
6
9

输出样例 #1

2 2
3 3
3 6

说明

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 $ .