2000 LSU Computer Science High School Programming Contest
Problem 7: The 3n+1 Problem (Judge Copy)

• Problem Statement
• Test Data 0
• Output for Test Data 0
• Test Data 1
• Output for Test Data 1
• Test Data 2
• Output for Test Data 2
• Test Data 3
• Output for Test Data 3

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Problem 7: The 3n+1 Problem (Judge Copy)

Problems in Computer Science are often classified as belonging to a certain class of problems (e.g., NP, Unsolvable, Recursive). In this problem you will be analyzing a property of an algorithm whose classification is not known for all possible inputs.

Consider the following algorithm:

 
	1.  input n

	2.  print n

	3.  if n = 1 then 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 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 before the 1 is printed. 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 .

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 10,000 and greater than 0. When you read the pair 0 0, you should stop processing.

You should process all pairs of integers and for each pair determine the maximum cycle length over all integers between and including i and j.

Output

For each pair of input integers i and j you should output i, j, and the maximum cycle length for integers between and including i and j. 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 i and j 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

1 10
100 200
201 210
900 1000
0 0

Sample Output

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

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Test Data 0

1 10 
100 200
201 210
900 1000
1 9999
1 1
9998 9998
0 0

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Output for Test Data 0

1 10 20
100 200 125
201 210 89
900 1000 174
1 9999 262
1 1 1
9998 9998 92

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Test Data 1

9000  9999 
15 20
14 17
3 5
500 521
500 505
505 510
510 515
515 520
520 521
0 0

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Output for Test Data 1

9000 9999 260
15 20 21
14 17 18
3 5 8
500 521 124
500 505 111
505 510 111
510 515 124
515 520 124
520 521 124

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Test Data 2

999 1111
9000 9056
14 29
0   0

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Output for Test Data 2

999 1111 169
9000 9056 185
14 29 112

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Test Data 3

89 111
2222 2333
7777 7788
0 0

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Output for Test Data 3

89 111 119
2222 2333 183
7777 7788 221

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