Unique Landmass Shapes

You are provided with a two-dimensional binary matrix grid of dimensions m x n, where each cell contains either 1 (representing land) or 0 (representing water). A landmass (or island) is defined as a contiguous region of land cells connected horizontally or vertically (4-directional connectivity). You may assume that all cells outside the grid boundaries are water.

Two landmasses are considered to have the same shape if and only if one can be translated (shifted horizontally and/or vertically) to perfectly overlap the other. Importantly, rotation and reflection (mirroring) do not make two landmasses identical—only pure translation counts.

Your task is to determine and return the total count of distinct landmass shapes present in the grid.

Key Insight: To identify whether two landmasses share the same shape, you must normalize their representation. One effective approach is to record the relative positions of all land cells within each landmass with respect to a consistent reference point (such as the top-left cell or the first cell discovered during traversal). Landmasses with identical normalized representations are considered duplicates.