An intelligence agency forms a code of two distinct digits selected from $0, 1, 2, \dots 9$ such that the first digit of the code is nonzero. The code, handwritten on a slip, can however potentially create confusion, when read upside down – for example, the code $91$ may appear as $16.$ How many codes are there for which no such confusion can arise?
- $80$
- $78$
- $71$
- $69$