The 3n+1 Problem (Hailstone Numbers)

Consider the following algorithm: 1. input n 2. print n 3. if (n == 1) STOP 4. if n is odd then n = 3n+1 5. else n = n/2 6. goto 2

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

    22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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 less than one million (and, in fact, for many more numbers than this.)

Given an input n, the number of numbers printed before and including the 1 is printed is called the cycle-length of n. In the example above, the cycle length of 22 is 16.

For any two numbers m and n you are to determine the maximum cycle length over all numbers between and including both m and n.

Input

The input will consist of a series of pairs of integers m and n, one pair of integers per line. All integers will be less than 10,000 and greater than 0. Input is terminated by a pair of numbers one of which is less than 0. You should process all pairs of integers and for each pair determine the maximum cycle length over all integers between and including m and n.

Output

For each pair of input integers m and n you should output m, n and the maximum cycle length for integers between and including m and n. These three numbers should be separated by at least one space with all three numbers on one line and with one line of output for each line of input. The integers m and n must appear in the output in the same order in which they appeared in the input and should be followed by the maximum cycle length (on the same line).

Sample Input

Sample Output

1 10 20
100 200 125
201 210 89
900 1000 174

Submit

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