# The 3n + 1 problem

Consider the following algorithm:

enter $n$

print $n$

if $n=1$ then STOP

if $n$ is odd then $n=3â‹…n+1$

else $n=n/2$

GOTO 2

Given the input $22$, the following sequence of numbers will be printed

It is conjectured that the algorithm above will terminate (when a $1$ is printed) for any integral input value. Despite the simplicity of the algorithm, it is unknown whether this conjecture is true. It has been verified, however, for all integers $n$ such that $0<n<1,000,000$ (and, in fact, for many more numbers than this.)

Given an input $n$, it is possible to determine the number of numbers printed (including the $1$). For a given $n$ this is called the cycle-length of $n$. In the example above, the cycle length of $22$ is $16$.

For any two numbers $i$ and $j$ you are to determine the maximum cycle length over all numbers between $i$ and $j$ inclusive.

## Input

The input will consist of a series of pairs of integers $i$ and $j$, one pair of integers per line. All integers will be less than $1,000,000$ and greater than $0$. You can assume that no operation overflows a $32$-bit integer.

## Output

For each pair of integers $i$ and $j$ you should output $i$ and $j$ in the same order in which they appeared in the input. Then print the maximum cycle length for integers between and including $i$ and $j$. For each test case print three numbers on one line, separating them by one space.