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.