Count Word Decompositions into Chemical Element Symbols

Given the set of chemical-element symbols and a target word, return the number of distinct ways the word can be segmented entirely into valid symbols. Requirements Input is the complete set of chemical-element symbols plus a target word. Count every distinct full decomposition of the word into valid symbols. A decomposition is valid only if the symbols cover the entire target in order. Clarify case handling because element symbols conventionally begin with an uppercase letter and may have a lowercase second letter. Examples Physics has four stated decompositions: P - H - Y - Si - C - S P - H - Y - Si - Cs P - H - Y - S - I - C - S P - H - Y - S - I - Cs The returned count is 4. Notes Confirm whether matching is case-sensitive and whether the caller supplies the symbol set or the implementation may treat the periodic table as fixed. The result counts decompositions, not merely whether at least one decomposition exists. Preparation Implement a suffix-count or prefix-count formulation and state what each state represents. Test a word with no decomposition, one decomposition, multiple decompositions, and overlapping one- and two-letter symbols.