Nikolay has a digital clock that displays time in 24-hour format, showing two integers: hours (from $00$ to~$23$) and minutes (from $00$ to $59$). For example, the clock can show \t{00:00}, \t{18:42}, or \t{23:59}.

The clock has two buttons that can be used for manual adjustment:
\begin{itemize}
\item Button A sets the clock forward by $1$ minute. For example, \t{05:33} becomes \t{05:34}, \t{16:59} becomes \t{17:00}, and \t{23:59} becomes \t{00:00}.
\item Button B sets the clock forward by $1$ hour. For example, \t{01:42} becomes \t{02:42}, and \t{23:14} becomes \t{00:14}.
% \item Button $B$ sets the clock backward by $1$ minute. For example, \t{21:09} becomes \t{21:08}, \t{10:00} becomes \t{09:59}, and \t{00:00} becomes \t{23:59}.
% \item Button $D$ sets the clock backward by $1$ hour. For example, \t{19:28} becomes \t{18:28}, and \t{00:56} becomes \t{23:56}.
\end{itemize}

Nikolay has noticed that the time on his clock does not look right. He wants to adjust the clock to the correct time by pressing the buttons as few times as possible.

Find the smallest number of button presses needed to adjust the clock.