Implement simplified Excel with SET/GET/SUM

Implement a simplified in-memory spreadsheet that supports three operations: SET, GET, and SUM, similar to basic Excel functionality.

Assumptions and requirements:

• The spreadsheet consists of cells identified by standard Excel-like coordinates:
  • Columns are single uppercase letters from 'A' to 'Z' .
  • Rows are integers from 1 to 1000 .
  • A cell ID is a string such as 'A1' , 'B2' , 'Z1000' .
• Each cell can either contain:
  • A numeric value (integer), or
  • A formula that is a sum of other cells or rectangular ranges of cells.

You must support the following operations:

1. SET(cellId, value)
   • Set the given cell to a numeric integer value.
   • Any existing formula or previous value in that cell is overwritten.
   • Return the value set.
2. GET(cellId)
   • Return the current evaluated integer value of the cell.
   • If the cell contains a formula (from a SUM operation), its value is the sum of its referenced cells, recursively evaluated.
3. SUM(cellId, refs)
   • cellId is the target cell where we store a formula.
   • refs is a list of references. Each reference is either:
     • A single cell ID, e.g. 'B2' , or
     • A rectangular range in the form 'A1:B2' , which represents all cells whose column is between A and B inclusive and whose row is between 1 and 2 inclusive.
   • Store in cellId a formula that is defined as the sum of all cells in refs (expanding ranges into the constituent cells).
   • Return the evaluated sum of that formula.

Behavioral example (your implementation should be consistent with this behavior):

• SET('A1', 1) → returns 1
• SET('B2', 2) → returns 2
• SUM('C1', ['A1:B2', 'B2']) → returns 5
• SUM('C1', ['B2']) → returns 2
• SET('C1', 5) → returns 5
• GET('C1') → returns 5
• SUM('D1', ['C1', 'A1']) → returns 6
• SET('A1', 10) → returns 10
• GET('C1') → returns 14 (because C1 still refers to B2 whose value is 2 , so its formula sum is 2 + 10 + 2 in the example sequence)

Additional requirements and edge cases:

• Updating a cell via SET or SUM must correctly affect any other cells whose formulas depend (directly or transitively) on that cell, so that subsequent GET calls return up-to-date values.
• There may be chains of dependencies, e.g. A1 used by B1 , which is used by C1 , etc.
• You must handle potential cycles in formulas. For example, if A1 depends on B1 and later B1 is defined to depend on A1 , there is a cycle.
  • Define and implement a reasonable behavior for cyclic dependencies (e.g., detect cycles during evaluation or update and prevent them, or return an error/special behavior). Clearly state your chosen behavior in code comments.
• Aim for an efficient implementation that avoids recomputing large dependency graphs from scratch on every GET .

Design and implement the data structures and methods to support these operations.