You are going to start from any number with distinct digits lower than four digits (such as $a$, $ab$, $abc$) and you will apply the rule below:
- Take the square any number you want in the number (you may take the square the number itself too). (such as $1(02)$ -> $14$, or $12(3)$ -> $129$ or $(13)$ -> $169$)
- Every number you found has to have distinct digits. (Fail example: $(12)3$-> $1443$ X)
- You may apply this as many times as you want. ($(13)$ -> $169$ then $(16)9$->$2569$)
What is the biggest final number you can have?