Virtual Rabbit (Small)

Alice just bought a virtual pet rabbit. The rabbit hops around on the screen and eats on the spot whenever she presses a button. Alice is fond of the rabbit, but she is busy and does not want to spend much time taking care of it. If the rabbit goes without food for too long, it dies and Alice loses the game.

Every day Alice gets up at time $G$, leaves for work at time $W$, comes back home at time $H$, and goes to bed at time $B$. She cannot feed the rabbit while she is at work or asleep, that is, during the intervals $[W, H)$ and $[B, G)$. The times $W$ and $B$ are not valid feeding times, while the times $H$ and $G$ are. In every other second Alice either presses the button and feeds the rabbit instantly, or does nothing.

The rabbit dies once more than $X$ seconds have passed since it last ate.

It is now 00:00:00 on day 0, and the mail carrier has just delivered the rabbit. The carrier presses the button at 00:00:00 even though Alice is asleep, and then leaves. Alice wants the rabbit to be alive at 00:00:00 on day $D$. If she can keep it alive, how few times can she feed it?

Stated precisely: number every second from 0, so that 00:00:00 on day 0 is second 0 and 00:00:00 on day $d$ is second $86400d$. Let $f_1 < f_2 < \dots < f_n$ be the seconds at which Alice feeds the rabbit, and let $f_0 = 0$ be the moment the mail carrier pressed the button. The rabbit is alive at 00:00:00 on day $D$ exactly when both conditions hold.

• $f_i - f_{i-1} \le X$ for every $i$ with $1 \le i \le n$
• $86400D - f_n \le X$

Every $f_i$ with $i \ge 1$ must be a second whose time of day falls in $[G, W)$ or in $[H, B)$. Find the smallest possible $n$.

The first line contains the number of test cases $T$. Then $T$ test cases follow, each consisting of 6 lines. The first five lines give the times $G$, $W$, $H$, $B$ and the length $X$ in "hh:mm:ss" format, one per line. The last line contains one integer $D$.

Limits

• $1 \le T \le 100$
• Alice always goes to bed before midnight and gets up after midnight, so $G$, $W$, $H$ and $B$ increase strictly within the same day.
• $\text{00:00:00} \le G < W < H < B \le \text{23:59:59}$
• $\text{00:00:00} < X \le \text{23:59:59}$
• $1 \le D \le 1000$

For each test case print one line in the format "Case #x: y", where $x$ is the test case number starting from 1 and $y$ is the minimum number of times Alice has to feed the rabbit. If there is no way to keep the rabbit alive at 00:00:00 on day $D$, then $y$ is $-1$.

In the first test case of the example, Alice can feed the rabbit at 08:00:00 and at 20:00:00 every day.

In the second test case of the example, the rabbit dies before Alice even wakes up on day 0.