A Clock With Blank Digits

Easy

A digital clock shows the time as "hh:mm", from "00:00" to "23:59". Some of its segments have gone dark, so some digits in the string display are replaced by ?. In how many ways can each ? be replaced by a digit from 0 to 9 so that the result is a real time of day?

Example 1

display="2?:4?" → 40

The hours can be 20 to 23 (4 options) and the minutes 40 to 49 (10 options): 4 · 10 = 40 in total.

Example 2

display="?9:?5" → 12

The hours are 09 or 19 (there is no 29) and the minutes 05, 15, …, 55. The answer is 2 · 6 = 12.

Example 3

display="13:07" → 1

Constraints

len(display) == 5, display[2] == ':'
The other characters are digits or ?
At least one replacement gives a valid time

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Topics

String Enumeration

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Input

display="2?:4?"

Expected

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