Juggler Sequence
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Juggler Sequence is a series of integer number in which the first term starts with a positive integer number a and the remaining terms are generated from the immediate previous term using the below recurrence relation:

 a_(k+1)={|_a_k^(1/2)_|   for even a_k; |_a_k^(3/2)_|   for odd a_k,

Given a number N your task is to print the space separated Juggler Sequence for this number as the first term of the sequence.

 

Examples:

Input: 9
Output: 9, 27, 140, 11, 36, 6, 2, 1
We start with 9 and use above formula to get
next terms.

Input: 6
Output: 6, 2, 1


Input:
The first line of input contains an integer T denoting the no of test cases. Then T test cases follow. Each line contains an integer N.

Output:
For each test case in a new line print the space separated juggler sequence for  number N as the first term of the sequence.

Constraints:
1<=T<=100
1<=N<=100

Example:
Input:

2
9
6
Output:
9  27 140 11 36 6 2 1
6 2 1

** For More Input/Output Examples Use 'Expected Output' option **

Author: Shubham Joshi 1


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