28.1 Problem

I remember that when I was in high school we used to have a lot of chemistry classes filled with problem solving. The key part of them was to calculate molar masses of different molecules. That segment, although essential, was rather boring. So I always wanted to have something that would speed up the calculations for me.

This time your job is to write a solver that will calculate a molar mass of a chemical formula. Make sure your solution works by using it on the following input:

• \(CH_{4}\) (methane, natural gas, fossil fuel),
• \(H_{2}O\) (water),
• \(HCl\) (hydrochloric acid produced in your stomach),
• \(CO_{2}\) (carbon dioxide, breath it out),
• \(C_{3}H_{8}\) (propane, natural gas, fossil fuel),
• \(C_{2}H_{5}OH\) (ethanol, is it time to quit drinking?),
• \((CH_{3})_{2}CO\) (acetone, nail polish remover),
• \(NaCl\) (sodium chloride, kitchen salt),
• \(CH_{3}COOH\) (acetic acid, it’s in vinegar),
• \(H_{2}CO_{3}\) (carbonic acid present in your blood),
• \(C_{6}H_{12}O_{6}\) (glucose, it gives you energy),
• \(C_{11}H_{12}N_{2}O_{2}\) (tryptophan, amino acid, builds proteins),
• \(CH_{3}(CH_{2})_{14}COOH\) (palmitic acid, builds fat),
• \(C_{34}H_{32}O_{4}N_{4}Fe\) (heme B, located in your red blood cells)
• \(Ca_{10}(PO_{4})_{6}(OH)_{2}\) (calcium hydroxyapatite found in your bones)
• \(C_{169719}H_{270466}N_{45688}O_{52238}S_{911}\) (titin, a protein that builds your muscles)

Below I paste the formulas and their masses for testing purposes.

formulas = ["CH4", "H2O", "HCl", "CO2", "C3H8", "C2H5OH", "(CH3)2CO",
            "NaCl", "CH3COOH", "H2CO3", "C6H12O6", "C11H12N2O2",
            "CH3(CH2)14COOH", "C34H32O4N4Fe", "Ca10(PO4)6(OH)2",
            "C169719H270466N45688O52238S911"]
masses = [16.043, 18.01528, 36.46, 44.01, 44.097, 46.069, 58.08, 58.443,
          60.052, 62.03, 180.156, 204.229, 256.43, 616.487, 1004.61,
          3_816_030]

A list of chemical elements and their masses is to be found, e.g. on this Wikipedia page.

For simplicity, you may assume, that a chemical formula (at least the one at a high school level) is composed of ASCII characters (capital/small letters + digits) and non-nested brackets.