Arcade Nameplate Entry Sequence

After a great run on a retro arcade cabinet, you get to type your name onto the high-score board one letter at a time using a single spring-loaded dial and a confirm button. Every time you start a brand-new letter slot, the very first press of the dial shows 'a' in that slot; every additional press before you confirm advances that same slot to the next letter of the alphabet, wrapping from 'z' back around to 'a'. Pressing confirm locks in whatever letter the slot currently shows -- it does not change what's on screen -- and the next dial press after a confirm always begins a fresh slot at 'a' again. Given the exact nameplate target you want typed, you always use the fewest dial presses possible for every letter (you press confirm the instant a slot shows the right letter, never pressing the dial more times than that letter needs). Reconstruct, in chronological order, every string that appears on the screen immediately after each dial press. (Confirm presses never change the screen, so they never add an entry to your list.)

Input format

A single line containing target, a non-empty string of lowercase English letters.

Output format

Line 1: an integer T, the total number of screen strings recorded. The next T lines: the screen's exact contents after each successive dial press, one per line, in chronological order.

Constraints

• 1 <= len(target) <= 50

ab

3
a
aa
ab

ba

3
a
b
ba