Count distinct island shapes in a grid

## Problem You are given an `m x n` grid of integers where `1` represents land and `0` represents water. An **island** is a group of horizontally or vertically adjacent `1`s. Two islands are considered the **same shape** if one can be translated (shifted up/down/left/right) to match the other **exactly**. Rotations and reflections **do not** count as the same shape. Return the number of **distinct island shapes** in the grid. ## Input - `grid`: `m x n` matrix of `0/1` ## Output - An integer: the number of distinct island shapes. ## Constraints - `1 <= m, n <= 500` (typical) - Grid may contain many islands ## Notes - Adjacency is 4-directional (up/down/left/right). - Translation allowed; rotation/reflection not allowed. ## Example If the grid contains two L-shaped islands in different locations, they count as **one** distinct shape.