Place Pieces on a Grid

Given integers `n` and `m`, and an ordered list `figures` where each element is one of `"A"`, `"B"`, `"C"`, `"D"`, or `"E"`, construct an `n x m` integer matrix `grid`. The grid starts with all values equal to `0`. Each figure has a fixed shape described by a binary matrix, where `1` means the figure occupies that cell and `0` means empty space: - `A = [[1]]` - `B = [[1, 1, 1]]` - `C = [[1, 1], [1, 1]]` - `D = [[1, 0], [1, 1], [1, 0]]` - `E = [[0, 1, 0], [1, 1, 1]]` Process the figures in the given order. For the figure at index `i`: 1. Try all possible top-left placement positions in row-major order: `(0, 0)`, `(0, 1)`, ..., `(0, m - 1)`, `(1, 0)`, ... . 2. A placement is valid if every `1` cell of the figure: - stays within the bounds of the grid, and - overlaps only cells that are currently `0`. 3. Place the figure at the first valid position. 4. Fill every occupied cell of that placed figure with the value `i + 1`. 5. If the figure cannot be placed anywhere, skip it and leave the grid unchanged. Return the final `grid`. Figures cannot be rotated or reflected.