Exchanging a coin

A bank will exchange a coin with the number n on it for three coins: n // 2, n // 3 and n // 4 (each divided and rounded down). You can also sell any coin for as many rupees as its number. You may exchange the new coins again, as often as you like. Return the most rupees you can end up with.

exchange(12)   # 13: 12 -> 6, 4, 3; sell all three
exchange(11)   # 11: 5 + 3 + 2 = 10, so sell it
exchange(24)   # 27

Limits

• n is from 0 to 10¹⁸ (a 1 followed by 18 zeros). A list with one entry for every number up to n would never fit in memory.
• The tests call your function many times in a row, with different values of n.