1427. Kaprekar Countdown

A puzzle magazine runs a digit game on four-digit numbers. Start with n, keeping exactly four digits with leading zeros (so 999 is treated as 0999). In one step, arrange the digits in descending order to get the larger number, arrange them in ascending order to get the smaller number, and replace the current number by their difference, again as four digits. Return how many steps are needed until the number becomes 6174, or 0 if n is already 6174. The digits of n are never all equal, and every such start reaches 6174 after a handful of steps, so the running time is O(1) with O(1) extra space.