A13706. Big Vova
编程题
普及/提高-
知识点
题目描述
Alexander is a well-known programmer. Today he decided to finally go out and play football, but with the first hit he left a dent on the new Rolls-Royce of the wealthy businessman Big Vova. Vladimir has recently opened a store on the popular online marketplace "Zmey-Gorynych", and offers Alex a job: if he shows his programming skills by solving a task, he'll work as a cybersecurity specialist. Otherwise, he'll be delivering some doubtful products for the next two years.
You're given $n$ positive integers $a_1, a_2, \dots, a_n$ . Using each of them exactly at once, you're to make such sequence $b_1, b_2, \dots, b_n$ that sequence $c_1, c_2, \dots, c_n$ is lexicographically maximal, where $c_i=GCD(b_1,\dots,b_i)$ - the greatest common divisor of the first $i$ elements of $b$ .
Alexander is really afraid of the conditions of this simple task, so he asks you to solve it.
A sequence $a$ is lexicographically smaller than a sequence $b$ if and only if one of the following holds:
- $a$ is a prefix of $b$ , but $a \ne b$ ;
- in the first position where $a$ and $b$ differ, the sequence $a$ has a smaller element than the corresponding element in $b$ .
You're given $n$ positive integers $a_1, a_2, \dots, a_n$ . Using each of them exactly at once, you're to make such sequence $b_1, b_2, \dots, b_n$ that sequence $c_1, c_2, \dots, c_n$ is lexicographically maximal, where $c_i=GCD(b_1,\dots,b_i)$ - the greatest common divisor of the first $i$ elements of $b$ .
Alexander is really afraid of the conditions of this simple task, so he asks you to solve it.
A sequence $a$ is lexicographically smaller than a sequence $b$ if and only if one of the following holds:
- $a$ is a prefix of $b$ , but $a \ne b$ ;
- in the first position where $a$ and $b$ differ, the sequence $a$ has a smaller element than the corresponding element in $b$ .
输入格式
Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 10^3$ ). Description of the test cases follows.
The first line of each test case contains a single integer $n$ ( $1 \le n \le 10^3$ ) — the length of the sequence $a$ .
The second line of each test case contains $n$ integers $a_1,\dots,a_n$ ( $1 \le a_i \le 10^3$ ) — the sequence $a$ .
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^3$ .
The first line of each test case contains a single integer $n$ ( $1 \le n \le 10^3$ ) — the length of the sequence $a$ .
The second line of each test case contains $n$ integers $a_1,\dots,a_n$ ( $1 \le a_i \le 10^3$ ) — the sequence $a$ .
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^3$ .
输出格式
For each test case output the answer in a single line — the desired sequence $b$ . If there are multiple answers, print any.
输入输出样例
输入 #1
7 2 2 5 4 1 8 2 3 3 3 8 9 5 64 25 75 100 50 1 42 6 96 128 88 80 52 7 5 2 4 8 16 17
输出 #1
5 2 8 2 1 3 9 3 8 100 50 25 75 64 42 128 96 80 88 52 7 17 2 4 8 16
说明/提示
In the first test case of the example, there are only two possible permutations $b$ — $[2, 5]$ and $[5, 2]$ : for the first one $c=[2, 1]$ , for the second one $c=[5, 1]$ .
In the third test case of the example, number $9$ should be the first in $b$ , and $GCD(9, 3)=3$ , $GCD(9, 8)=1$ , so the second number of $b$ should be $3$ .
In the seventh test case of the example, first four numbers pairwise have a common divisor (a power of two), but none of them can be the first in the optimal permutation $b$ .
In the third test case of the example, number $9$ should be the first in $b$ , and $GCD(9, 3)=3$ , $GCD(9, 8)=1$ , so the second number of $b$ should be $3$ .
In the seventh test case of the example, first four numbers pairwise have a common divisor (a power of two), but none of them can be the first in the optimal permutation $b$ .