123 456 789
Bessie is trying to type out a given phone number in a hurry, so she decides to save time by pressing multiple buttons at the same time with one of her hooves. Specifically, Bessie's hoof might press a single digit, two digits that share a side (for twelve possible pairs in total), or four digits that form a square (1245, 2356, 4578, or 5689).
For example, if the phone number Bessie is trying to type is 123659874, she might attempt to save time by
Unfortunately, Bessie drastically overestimated her skill at performing this task - if Bessie's hoof pressess multiple buttons at the same time, then all of the digits will be typed in arbitrary order. So if Bessie attempts the above sequence of presses, she may end up typing 123596847 or 213659874 instead (or one of many other possibilities).
Given a sequence of digits that Bessie has typed, count the number of phone numbers that she could have been trying to type modulo $10^9+7$.
**Note: the time limit for this problem is 1s**
The next $T$ lines each contain a nonempty string of the digits 1 through 9. It is guaranteed that the total length of these strings does not exceed $10^5$.
5 1478 4455 5968 31313211 123659874
5 2 24 3 255
For the first case, Bessie might be trying to type any of the following five phone numbers:
1478 1487 4178 4187 1748
For example, if Bessie was trying to type 4187, she might have tried pressing 1 and 4 at the same time and then tried pressing 7 and 8 at the same time.
For the third case, as the numbers form a square, Bessie might have been trying to type any permutation of the input sequence.
Problem credits: Nick Wu