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Number of Atoms

XPChallenge Points: 30
levelLevel: Hard

A chemical formula string represents different elements and their quantities.
Each element begins with a capital letter and may include lowercase letters after it.
A number following an element indicates how many times that element appears—if no number is present, the quantity is 1.

Formulas may contain:

  • Simple sequences, like "NaCl"

  • Repeated groups, like "H2O" or "C6H12O6"

  • Nested parentheses, e.g. "(OH)2" or "K4(ON(SO3)2)2"

Your task is to compute how many times each atom appears in the whole formula.
Finally, return a string that lists all atom names in sorted order, and append their counts (except when the count is 1).

All final quantities will fit in a 32-bit integer.

Example 1:

Input: formula = "C6H5OH"

Output: "C6H6O"

Example 2:

Input: formula = "Fe2(SO4)3"

Output: "Fe2O12S3"

Explanation:

Fe appears 2 times SO₄ is repeated 3 times → O: 4×3 = 12, S:1×3 = 3

Example 3:

Input: formula = "Al2(OH)5Mg3"

Output: "Al2H5Mg3O5"

Explanation:

Counts: Al:2, O:5, H:5, Mg:3.

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