In a previous contest, a question was asked about determining how many days apart two dates were, ignoring leap years. This question is essentially the same, except it includes leap years. In addition, this question only asks for the count of days from $d a t e 1$ to $d a t e 2$, and $d a t e 2$ will always be after $d a t e 1$. Take in two dates in the form of month-name day-number, year. Then print out the number of days from the first date to the second one, and make sure that your calculation includes the addition of days added by leap years.
The first line contains the first date in the form of month day, year. The month is provided as a capitalized name, and not a number. The second line contains the second date in the same form.
A single integer representing the number of days from the first date to the second.
The second date will always be after the first. Make sure to consider leap years. If you have difficulty with the input, be sure to carefully follow the formatting.
## Input
The first line contains the first date in the form of month day, year. The month is provided as a capitalized name, and not a number. The second line contains the second date in the same form.
## Output
A single integer representing the number of days from the first date to the second.
[samples]
## Note
The second date will always be after the first. Make sure to consider leap years. If you have difficulty with the input, be sure to carefully follow the formatting.
**Definitions**
Let $ D_1 = (m_1, d_1, y_1) $ and $ D_2 = (m_2, d_2, y_2) $ be two dates, where:
- $ m_i \in \{\text{January}, \text{February}, \dots, \text{December}\} $ is the month name,
- $ d_i \in \mathbb{Z} $, $ 1 \leq d_i \leq \text{daysInMonth}(m_i, y_i) $ is the day number,
- $ y_i \in \mathbb{Z} $, $ y_i \geq 1 $ is the year.
Let $ \text{isLeap}(y) = \begin{cases}
1 & \text{if } y \bmod 4 = 0 \text{ and } (y \bmod 100 \ne 0 \text{ or } y \bmod 400 = 0) \\
0 & \text{otherwise}
\end{cases} $
Let $ \text{daysInMonth}(m, y) $ be the number of days in month $ m $ in year $ y $, with February having 29 days if $ \text{isLeap}(y) = 1 $, else 28.
Let $ \text{dayOfYear}(m, d, y) $ be the ordinal day of the year for date $ (m, d, y) $, computed by summing days in all prior months plus $ d $.
**Constraints**
1. $ D_2 $ occurs strictly after $ D_1 $: $ (y_2 > y_1) \lor (y_2 = y_1 \land \text{dayOfYear}(m_2, d_2, y_2) > \text{dayOfYear}(m_1, d_1, y_1)) $
**Objective**
Compute the total number of days from $ D_1 $ to $ D_2 $:
$$
\text{Days} = \left( \sum_{y=y_1}^{y_2-1} (365 + \text{isLeap}(y)) \right) + \text{dayOfYear}(m_2, d_2, y_2) - \text{dayOfYear}(m_1, d_1, y_1)
$$