A15084 | The Clock

Victor has a [24-hour clock](https://en.wikipedia.org/wiki/24-hour_clock) that shows the time in the format "HH:MM" (00 $\le$ HH $\le$ 23, 00 $\le$ MM $\le$ 59). He looks at the clock every $x$ minutes, and the clock is currently showing time $s$ .

How many different palindromes will Victor see in total after looking at the clock every $x$ minutes, the first time being at time $s$ ?

For example, if the clock starts out as 03:12 and Victor looks at the clock every $360$ minutes (i.e. every $6$ hours), then he will see the times 03:12, 09:12, 15:12, 21:12, 03:12, and the times will continue to repeat. Here the time 21:12 is the only palindrome he will ever see, so the answer is $1$ .

A palindrome is a string that reads the same backward as forward. For example, the times 12:21, 05:50, 11:11 are palindromes but 13:13, 22:10, 02:22 are not.

The first line of the input contains an integer $t$ ( $1 \leq t \leq 100$ ) — the number of test cases. The description of each test case follows.

The only line of each test case contains a string $s$ of length $5$ with the format "HH:MM" where "HH" is from "00" to "23" and "MM" is from "00" to "59" (both "HH" and "MM" have exactly two digits) and an integer $x$ ( $1 \leq x \leq 1440$ ) — the number of minutes Victor takes to look again at the clock.

For each test case, output a single integer — the number of different palindromes Victor will see if he looks at the clock every $x$ minutes starting from time $s$ .