Balance an equation by search

A computer can balance an equation by trying small whole numbers in front of each formula, smallest first, until the atoms match. You will write the counting, the search, and then use it on propane.

The idea. A coefficient multiplies every atom in its formula. An equation is balanced when each element has the same count on both sides.

Your tasks.

1. In side_total, add c * n to total[element] for every atom of every formula.
2. In balance, return a, b as soon as the two sides have equal totals.
3. Find oxygen_coef, the number in front of $\text{O}_2$ when propane burns: $\text{C}_3\text{H}_8 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$.