Given $$the $$dictionary $$below $$compress $$the $$input $$text $$stream $$using $$LZW $$

compression $$and $$show $$the $$compressed $$output $$text$.$

Input $$text: $$a $$a $$b $$a $$b $$b $$a $$b $$b $$a $$a $$b $$b $$b

key $$a $$

$=$

$$code $$

$0$

$$

key $$b $$

$=$

$$code $$

$1$