Generating Numbers
Applying the steps below, you will generate a number, on the condition that every digit of a number produced in each step is different from its other digits.

1. Write down a number with one, two or three digits.
2. Delete at most three consecutive digits and in the places of the deleted digits place the square of the number formed by these digits.
3. For the number you get, repeat steps two and three. If you cannot get a number that satisfies the conditions, stop.

What is the largest number that can be generated through this mechanism?

Example: 307, 3(07), 349, 3(4)9, 3169, ...