Problem D
Dating time
Our two lovebirds, Banmuon and Henho want to go on a date. However, they are afraid that their friends or families may find out. Thus, they have decided to setup their dating time using the following secret methods:
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Banmuon will send Henho a string with format h1:m1 h2:m2 alpha where h1:m1 and h2:m2 represent some time in $24$-hour format. $alpha$ is an integer between $0$ and $180$ and is divisible by $90$.
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Their dating time will be some time between h1:m1 and h2:m2, where the two clock hands, hour and minute, forms an angle equals to $alpha$ degree.
However, there is a problem: their dating time may not be unique! Please help Banmuon and Henho figure out how many possible valid dating times there are.
Note
In this problem, we use a normal analog clock:
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The minute hand rotates continuously. It takes $60$ minutes to make one complete rotation (from $12$ to $12$).
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The hour hand rotates continuously. It takes $12$ hours to make one complete rotation (from $12$ to $12$).
Input
The first line of input contains a single integer $t$ $(1 \le t \le 100)$ — the number of test cases.
$t$ lines follow, each line has format: h1:m1 h2:m2 alpha $(0 \le h_1, h_2 \le 23, 0 \le m_1, m_2 \le 59, 0 \le alpha \le 180)$. $h_1$, $m_1$, $h_2$ and $m_2$ will have exactly two digits, with leading zero if they are less than $10$.
It is guaranteed that h1:m1 is less than or equal to h2:m2 and $alpha$ is divisible by $90$.
Output
For each test case, print the number of instants when the two clock hands form an angle equals to $alpha$ degrees, between h1:m1 and h2:m2, inclusive.
Explanation of Sample input
In the first test case, there are $22$ instants when the two clock hands form a $0$-degree angle. Below are the first $11$ instants.
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00:00
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01:05 and $\frac{5}{11}$ minute.
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02:10 and $\frac{10}{11}$ minute.
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03:16 and $\frac{4}{11}$ minute.
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04:21 and $\frac{9}{11}$ minute.
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05:27 and $\frac{3}{11}$ minute.
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06:32 and $\frac{8}{11}$ minute.
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07:38 and $\frac{2}{11}$ minute.
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08:43 and $\frac{7}{11}$ minute.
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09:49 and $\frac{1}{11}$ minute.
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10:54 and $\frac{6}{11}$ minute.
| Sample Input 1 | Sample Output 1 |
|---|---|
3 00:00 23:59 0 00:00 23:59 90 18:00 18:01 180 |
22 44 1 |
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