# Collatz Conjecture

Time Limit: 10 Seconds Memory Limit: 131072 KB

The Collatz conjecture which is also known as the 3*n*+1 conjecture is a very well known and old conjecture in mathematics. The conjecture is as follows. Take any natural number *n*. If n is even, divided by two to get *n*/2 and if *n* is odd number greater than 1, triple it and add one to obtain 3*n*+1. Repeat this process to get a sequence of natural numbers known as the Hailstone sequence. The conjecture is that no matter what number you start, you always reach 1. The hailstone sequence for *n*=3 is "3,10,5,16,8,4,2,1". Paul Erdos said “Mathematics is not yet ripe for such problems” and offered $500 for its solution. Now it's time to show Erdos that the Collatz conjecture can be proved for small numbers in 11^{th} Iran Internet Programming Contest. You are to write a program that computes the length of the Hailstone sequence for the given *n*.

## Input

There are multiple test cases in the input. Each test case consists of a line containing a non-negative integers 0≤*n*≤100. The input terminates with “0” which should not be processed.

## Output

For each test case, output the length of the Hailstone sequence in one line.

## Sample Input

1 2 3 0

## Sample Output

1 2 8Submit

Source: 11th Iran Nationwide Internet Contest