Consider a simple crossword puzzle formed of four five-letter words, joined at the corners by their initial and final letters. For example:

   B A S I C
   R       A
   E       D
   A       E
   D E B I T

In classic crossword style, the first word across (BASIC) would be 1 across, BREAD would be 1 down, CADET would be 2 down, and DEBIT would be 3 across.

Now, consider a similar crossword with the following clues:

Across:
1. Caesar, for one
3. Grout and mortar guy

Down:
1. _____ whale
2. Anagram of "dinar"

        ¹       ²
                 
                 
                 
        ³        

There are two independent solutions. Find both.