There are only four neighbourhoods in a city - Levmisto, Tyhrmisto, Pesmisto and Kitmisto. During the onset of a pandemic, the number of new cases of a disease in each of these neighbourhoods was recorded over a period of five days. On each day, the number of new cases recorded in any of the neighbourhoods was either $0,1,2$ or $3$.
The following facts are also known:
1. There was at least one new case in every neighbourhood on Day $1$.
2. On each of the five days, there were more new cases in Kitmisto than in Pesmisto.
3. The number of new cases in the city in a day kept increasing during the five-day period. The number of new cases on Day $3$ was exactly one more than that on Day $2$.
4. The maximum number of new cases in a day in Pesmisto was $2$, and this happened only once during the five-day period.
5. Kitmisto is the only place to have $3$ new cases on Day $2$.
6. The total numbers of new cases in Levmisto, Tyhrmisto, Pesmisto and Kitmisto over the five-day period were $12,12, 5$ and $14$ respectively.
On which day(s) did Pesmisto not have any new case?
- Both Day $2$ and Day $3$
- Only Day $3$
- Only Day $2$
- Both Day $2$ and Day $4$