Number Chains

Given a number, we can form a number chain by

1. arranging its digits in descending order
2. arranging its digits in ascending order
3. subtracting the number obtained in (2) from the number obtained (1) to form a new number 4. and repeat these steps unless the new number has already appeared in the chain Note that 0 is a permitted digit. The number of distinct numbers in the chain is the length of the chain. You are to write a program that reads numbers and outputs the number chain and the length of that chain for each number read. Input The input consists of a sequence of positive numbers, all less than 109, each on its own line, terminated by ‘0’. The input file contains at most 5000 numbers. Output The output consists of the number chains generated by the input numbers, followed by their lengths exactly in the format indicated below. After each number chain and chain length, including the last one, there should be a blank line. No chain will contain more than 1000 distinct numbers. Sample Input 123456789 1234 444 0 Sample Output Original number was 123456789 987654321 - 123456789 = 864197532 987654321 - 123456789 = 864197532 Chain length 2 Original number was 1234 4321 - 1234 = 3087 8730 - 378 = 8352 8532 - 2358 = 6174 7641 - 1467 = 6174 Chain length 4 Original number was 444 444 - 444 = 0

2/2 0-0=0 Chain length 2