Implement string/matrix simulations and counting pairs

You are given several independent implementation-focused tasks. For each task, write a function that returns the required value. ## Task 1 — Count matching 3-character windows (case-insensitive) Given a string `s`, consider every contiguous substring of length 3: `s[i..i+2]` for `0 ≤ i ≤ len(s)-3`. Count how many such windows satisfy: - `lower(s[i]) == lower(s[i+2])` (case-insensitive comparison) **Output:** an integer count. **Notes:** - If `len(s) < 3`, the answer is `0`. --- ## Task 2 — Grid “match-3” explosion with gravity You are given an `m x n` integer matrix `grid` where each integer represents a “color”. A cell `(r, c)` has up to 4 orthogonal neighbors: up, down, left, right. ### Explosion rule A cell `(r, c)` is considered a **trigger** if **at least 2** of its orthogonal neighbors have the **same value** as `grid[r][c]`. When a cell triggers, the cell itself and all orthogonal neighbors that match its value are marked to be removed. All removals for the step happen **simultaneously**. ### Gravity rule After removals, the removed positions become empty. Then, for each column independently: - All remaining values in the column “fall” downward (preserving their relative order). - Empty cells are filled at the top with `0`. ### Iteration Repeat **Explosion → Gravity** until no more cells trigger. **Output:** the final matrix after the process stabilizes. **Clarifications:** - `0` is treated as an empty cell after gravity; it does **not** participate in explosions. --- ## Task 3 — Count ordered pairs that form a target string Given a list of strings `words` of length `n` and a target string `target`, count the number of **ordered** index pairs `(i, j)` such that: - `0 ≤ i, j < n` - `i != j` - `words[i] + words[j] == target` **Output:** an integer count. **Important:** Ordered pairs are distinct, so `(i, j)` and `(j, i)` are counted separately when both satisfy the condition.