Implement list and grid transformation tasks

You are given three independent coding tasks (as in an online assessment). Implement each as a separate function.

1) Uppercase–lowercase difference

Input: A list of characters chars (each element is a 1-length string).

Output: An integer equal to:

$(\#\text{uppercase letters}) - (\#\text{lowercase letters})$

Notes:

• Use typical letter checks (e.g., isupper() , islower() semantics).
• Non-letters (digits, punctuation, whitespace, etc.) do not affect the result.

2) Repartition numbers into two lists, then merge

Input: An integer array nums.

Process: Iterate nums from left to right and build two lists A and B. For each number x:

1. Let maxA be the maximum value currently in A (or $-\infty$ if A is empty). Let maxB be the maximum value currently in B (or $-\infty$ if B is empty).
2. If maxA > x or maxB > x , append x to the list whose current maximum is larger:
   • if maxA >= maxB , append to A ; else append to B .
3. Otherwise (i.e., x is at least as large as both current maxima), append x to the shorter list (if tied, append to A ).

Output: Return the concatenation A + B.

3) Balloon explosion in an n×n grid with gravity

Input: An n × n integer matrix grid where each positive integer represents a balloon color/label, and 0 represents an empty cell.

Explosion rule (4-neighborhood): For any cell (r, c) with value v > 0, count how many of its up/down/left/right neighbors also have value v. If that count is ≥ 2, then the balloon at (r, c) explodes.

• All explosions in a round happen simultaneously (decide based on the grid state at the start of the round).
• Exploded cells become 0 .

Gravity rule: After explosions, apply gravity column by column: within each column, all non-zero values fall downward to fill empty spaces, preserving their relative order (stable fall).

Repeat: Repeat “explosion round → gravity” until a full round causes no explosions.

Output: Return the final stabilized grid.

Clarifications:

• Only 4-direction adjacency counts (no diagonals).
• Edge cells have fewer neighbors.