Compute nested depth sum and grid distance

## Problem A: Weighted sum of integers in a nested list You are given a nested list structure that may contain integers or other nested lists. Define the **depth** of top-level elements as 1, their children as depth 2, etc. **Task:** Compute the sum of each integer multiplied by its depth. **Input:** - A nested list, e.g. `[1, [4, [6]]]` **Output:** - An integer weighted sum **Example:** - Input: `[1, [4, [6]]]` - `1` at depth 1 → `1*1` - `4` at depth 2 → `4*2` - `6` at depth 3 → `6*3` - Total = `1 + 8 + 18 = 27` **Constraints (typical):** - Total number of integers across all nesting: up to ~1e5 - Nesting depth may be up to ~1e3 --- ## Problem B: Best empty cell minimizing distance to all buildings You are given an `m x n` grid with values: - `0` = empty land (you may start here) - `1` = building - `2` = obstacle (cannot pass) Movement is 4-directional (up/down/left/right). Distance is the number of steps along empty cells (you cannot pass through obstacles or buildings). **Task:** Choose an empty cell `0` such that the **sum of shortest path distances** from that cell to **every** building is minimized. Return that minimum sum. If there is no empty cell from which all buildings are reachable, return `-1`. **Input:** - `grid`: `m x n` integer matrix **Output:** - Minimum possible sum distance, or `-1` **Example:** - `grid = [[1,0,2,0,1],[0,0,0,0,0],[0,0,1,0,0]]` → output `7` (one optimal empty cell has total distance 7) **Constraints (typical):** - `1 <= m,n <= 50`