A calculator toy shows a row of digits digits. Between each pair of neighbouring digits you may put
+, -, *, or nothing (which glues the digits into a longer number). A multi-digit number may not
start with 0. Multiplication binds tighter than addition and subtraction, as usual. Count how many
different formulas evaluate to exactly target.
Examples
Input: digits = "232", target = 8
Output: 2
Explanation: 2*3+2 and 2+3*2.
Input: digits = "10", target = 1
Output: 2
Explanation: 1+0 and 1-0.
Input: digits = "05", target = 5
Output: 1
Explanation: 0+5 works, "05" is not allowed as a number.
Constraints
1 <= len(digits) <= 9,-10**9 <= target <= 10**9
Goals
- Enumerate operator placements while evaluating incrementally
- Handle multiplication precedence by tracking the last term