A15665. Minimum LCM

You are given an integer $n$ .

Your task is to find two positive (greater than $0$ ) integers $a$ and $b$ such that $a+b=n$ and the least common multiple (LCM) of $a$ and $b$ is the minimum among all possible values of $a$ and $b$ . If there are multiple answers, you can print any of them.

The first line contains a single integer $t$ ( $1 \le t \le 100$ ) — the number of test cases.

The first line of each test case contains a single integer $n$ ( $2 \le n \le 10^9$ ).

For each test case, print two positive integers $a$ and $b$ — the answer to the problem. If there are multiple answers, you can print any of them.

In the second example, there are $8$ possible pairs of $a$ and $b$ :

- $a = 1$ , $b = 8$ , $LCM(1, 8) = 8$ ;
- $a = 2$ , $b = 7$ , $LCM(2, 7) = 14$ ;
- $a = 3$ , $b = 6$ , $LCM(3, 6) = 6$ ;
- $a = 4$ , $b = 5$ , $LCM(4, 5) = 20$ ;
- $a = 5$ , $b = 4$ , $LCM(5, 4) = 20$ ;
- $a = 6$ , $b = 3$ , $LCM(6, 3) = 6$ ;
- $a = 7$ , $b = 2$ , $LCM(7, 2) = 14$ ;
- $a = 8$ , $b = 1$ , $LCM(8, 1) = 8$ .

In the third example, there are $5$ possible pairs of $a$ and $b$ :

- $a = 1$ , $b = 4$ , $LCM(1, 4) = 4$ ;
- $a = 2$ , $b = 3$ , $LCM(2, 3) = 6$ ;
- $a = 3$ , $b = 2$ , $LCM(3, 2) = 6$ ;
- $a = 4$ , $b = 1$ , $LCM(4, 1) = 4$ .