Description

Kaprekar was a mathematician. He discovered that for any four-digit number not composed of completely identical digits: if you reorder its digits to form the largest number and the smallest number, then subtract the smaller from the larger; if the difference has fewer than four digits, pad with leading zeros; and repeat this process, it will eventually become a fixed number $6174$, which is the Kaprekar constant. For example:

$4321-1234=3087$.

$8730-378=8352$.

$8532-2358=6174$.

$7641-1467=6174$.

If a K-digit number is processed in the same way, it does not become a single number but forms a cycle among several numbers, called the Kaprekar Waltz. For example, for the five-digit number $54321$:

$54321-12345=41976$.

$97641-14679=82962$.

$98622-22689=75933$.

$97533-33579=63954$.

$96543-34569=61974$.

$97641-14679=82962$.

We call 82962, 75933, 63954, 61974 the repeating cycle, i.e., the Kaprekar Waltz.

Input Format

Multiple lines. Each line contains a starting integer $n$ for which to find the "Kaprekar Waltz" ($n<2^{31}$).

Output Format

For each input integer, output the corresponding cycle terms on one line, separated by spaces.

4321
54321

6174
82962 75933 63954 61974

Hint

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