Collatz Conjecture Analysis

Given a positive integer \( n \), perform an analysis on its Collatz sequence. The Collatz sequence is defined by the following recurrence relation:

\( n_{next} = \begin{cases}\frac{n}{2} &\text{if } n \text{ is even} \\ 3n+1 &\text{if } n \text{ is odd}\end{cases}\)

Your task is to compute the following:

1. The number of steps required for \( n \) to reach 1.
2. The maximum value encountered in the sequence.
3. The full Collatz sequence starting from \( n \) and ending at 1.

Note: The step count does not include the starting number \( n \) but counts each transition until 1 is reached.

inputFormat

A single positive integer ( n ) provided in one line from standard input.

outputFormat

Print three lines to standard output:

1. The first line contains the number of steps required for ( n ) to reach 1.
2. The second line contains the maximum value encountered in the sequence.
3. The third line contains the full Collatz sequence as space-separated integers.## sample

13

9
40
13 40 20 10 5 16 8 4 2 1