The air-conditioner $\text{(AC)}$ in a large room can be operated either in $\text{REGULAR}$ mode or in $\text{POWER}$ mode to reduce the temperature.
If the $\text{AC}$ operates in $\text{REGULAR}$ mode, then it brings down the temperature inside the room (called inside temperature) at a constant rate to the set temperature in $1$ hour. If it operates in $\text{POWER}$ mode, then this is achieved in $30$ minutes.
If the $\text{AC}$ is switched off, then the inside temperature rises at a constant rate so as to reach the temperature outside at the time of switching off in $1$ hour.
The temperature outside has been falling at a constant rate from $7$ $\mathrm{pm}$ onward until $3$ $\mathrm{am}$ on a particular night. The following graph shows the inside temperature between $11$ $\mathrm{pm}(23: 00)$ and $2$ $\mathrm{am}(2: 00)$ that night.
The following facts are known about the $\text{AC}$ operation that night.
- The $\text{AC}$ was turned on for the first time that night at $11$ $\mathrm{pm}$ $(23:00)$.
- The $\text{AC}$ setting was changed (including turning it on/off, and/or setting different temperatures) only at the beginning of the hour or at $30$ minutes after the hour.
- The $\text{AC}$ was used in $\text{POWER}$ mode for longer duration than in $\text{REGULAR}$ mode during this $3$-hour period.
What was the maximum difference between temperature outside and inside temperature, in degree Celsius, between $11:01$ $\mathrm{pm}$ and $1:59$ $\mathrm{am}$?