Crossword Word Filling

You are given an m x n board representing a crossword puzzle. Each cell is either a black square '#' or a white square '.'. You are also given a list of lowercase English words. Your task is to place every word into the crossword exactly once, filling only white squares, so that every maximal horizontal or vertical run of white squares (length ≥ 2) is completely occupied by one of the given words. Words may intersect only if the shared letter matches. Return true if such a placement exists, otherwise return false.