Ambiguous Coordinates

We had some 2-dimensional coordinates, like "(1, 3)" or "(2, 0.5)". Then, we removed all commas, decimal points, and spaces and ended up with the string s.

Return a list of strings representing all possibilities for what the original coordinates could have been.

The original representation never had extraneous zeroes, so it never started with numbers like "00", "0.0", "0.00", "1.0", "001", "00.01", or any other number that can be represented with fewer digits. Also, a decimal point within a number never occurs without at least one digit before it, so the original representation never started with numbers like ".1".

The final answer list can be returned in any order. All coordinates in the final answer have exactly one space between them, occurring after the comma.

Example 1
Inputs = "(123)"
Output["(1, 2.3)","(1, 23)","(1.2, 3)","(12, 3)"]
These are all valid ways to insert the comma, optional decimal points, and required space without creating numbers with extraneous zeroes.
Example 2
Inputs = "(0123)"
Output["(0, 1.23)","(0, 12.3)","(0, 123)","(0.1, 2.3)","(0.1, 23)","(0.12, 3)"]
0.0, 00, 0001 or 00.01 are not allowed.

Constraints

  • 4 <= s.length <= 12
  • s[0] == '(' and s[s.length - 1] == ')'.
  • The rest of s are digits.

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