P5440 [XR-2] Miracle

> Those who believe in miracles are, themselves, as amazing as miracles. — Diya, *Star Odyssey*.

We define a **date** as an 8-digit number. Digits $1 \sim 4$ form the year, digits $5 \sim 6$ form the month, and digits $7 \sim 8$ form the day. If a part has fewer digits, it is padded with $0$. Also, the day represented by the date must really exist, and the year ranges from $1 \sim 9999$. All miracle dates share the same property: the 2-digit number formed by the “day”, the 4-digit number formed by “month + day”, and the 8-digit number formed by “year + month + day” are all **prime numbers**. However, not every date with this property will necessarily have a miracle. Now you are given a date that may have a miracle, but unfortunately this date is incomplete: among the 8 digits, some digits may be unknown. You need to determine how many possible dates it could be, so that you can be fully prepared to welcome the miracle.

**This problem has multiple test cases.** The first line contains a positive integer $T$, the number of test cases. The next $T$ lines each contain an 8-character string. If the $i$-th character is `-`, it means the $i$-th digit of the date is unknown; otherwise, it means the $i$-th digit of the date is the digit at position $i$ in the string.

For each test case, output one integer per line, representing the answer.

[Sample $1$ Explanation] The 6 possible dates for `53-7-3-7` are: ```plain 53070307 53070317 53170307 53370307 53570317 53770307 ``` [Constraints] There are $10$ test points in total. Let $c$ be the number of `-` characters in the 8-character string. For the first $9$ test points, in the $i$-th test point it is guaranteed that $c = i - 1$. For $100\%$ of the testdata, it is guaranteed that $1 \le T \le 10$. Translated by ChatGPT 5