Randomly Generate a Fully-Populated Grid with 4 Equal-Size Connected Components

Problem Given an m × n grid, fill it completely with 4 tokens labeled 1, 2, 3, 4 such that: Every cell is assigned exactly one token (no empty cells). Each token must occupy the same number of cells. Therefore m*n must be divisible by 4 (otherwise there is no solution). For each token, all its cells must form one connected component. Connectivity is 4-directional only (up, down, left, right). Task: Design and implement an algorithm that randomly generates a grid satisfying all constraints. If a single attempt fails to produce a valid grid, you may retry, but describe the retry strategy. Input Two integers m, n. Output Print an m × n integer grid (each row has n integers), each in {1,2,3,4}, satisfying the constraints. Constraints (if not explicitly provided, you may assume) Suggested: 1 ≤ m, n ≤ 30. Example (illustrative only) Input: 4 4 Possible output: 1 1 2 2 1 3 3 2 4 3 2 2 4 4 4 4 (The example is only for output format; actual output must have equal counts and each token connected.) Example Input 4 4 Output (any valid 4x4 grid with each token appearing 4 times and each token 4-connected)