Backstage Countdown Minimum Nudges

Before every performance, the stage manager's countdown clock must be advanced from whatever time it currently displays to the exact cue time written on the show's timing sheet. The clock has exactly four nudge buttons, which move the displayed time forward by 1, 5, 15, or 60 minutes respectively, wrapping back around to 00:00 after 23:59. Given the clock's current display and the required cue time, determine the fewest button presses needed to reach the cue time exactly (the clock only ever moves forward in time, and may wrap past midnight).

Input format

Line 1: the current time as a string HH:MM (24-hour clock, 00 <= HH <= 23, 00 <= MM <= 59). Line 2: the target cue time as a string HH:MM in the same format.

Output format

A single integer: the minimum number of nudges required to advance the clock from the current time to the cue time.

Constraints

• Both lines are valid 24-hour timestamps in HH:MM format.
• The current time and cue time may be equal, in which case the answer is 0.
• The cue time may be earlier in the day than the current time, requiring the clock to wrap past midnight.

02:30
04:35

3

11:00
11:01

1