Grid Flower Placement with Row/Column Uniqueness and House Adjacency Constraints

Given an N x N grid: 'H' denotes a house '0' denotes an empty cell Place flowers 'F' on some cells such that: Each row contains exactly one 'F'. Each column contains exactly one 'F'. For every house 'H', among its 4-directional neighbors (up/down/left/right), there must be exactly one flower 'F' (consider only neighbors within bounds). Return any valid resulting N x N grid containing 'H', '0', and 'F'. If no solution exists, return/output empty (e.g., empty grid or print IMPOSSIBLE). Example input: H000 H000 000H 0000 Return any valid grid if one exists. Constraints: 1 <= N <= ? (not specified in the post; treat as a backtracking/DFS problem) Note: You can only place 'F' on cells that are originally '0' (do not overwrite houses). Example Input 4 H000 H000 000H 0000 Output <any valid grid or IMPOSSIBLE>