This problem was inspired by another jovial Numberphile video “Primes on the Moon” by Neil Sloane that you should watch first to get an idea of how this wacky “lunar arithmetic” works.

Formerly known as “dismal arithmetic”, addition and multiplication of natural numbers are redefined so that adding two digits means taking their maximum, whereas multiplying two digits means taking their minimum. For example, 2 + 7 = 7 + 2 = 7 and 2 × 7 = 7 × 2 = 2. Unlike ordinary addition, there can never be a carry to the next column of digits, no matter how many individual digits are added together in that column. For numbers that consist of several digits, addition and multiplication work exactly as you learned back in grade school, except that the shifted digit columns from lunar multiplication of the individual digits are added in the same lunatic fashion. Let's look again at the example:

Input: Two integers (number).

Output:...