In Byteland they have a very strange monetary system. Each Bytelandian gold coin has an integer number written on it. A coin $$n$$ can be exchanged in a bank into three coins: $$\frac{n}{2}$$, $$\frac{n}{3}$$ and $$\frac{n}{4}$$. These three numbers are rounded down, since the banks have to make a profit somehow.
You can also sell Bytelandian coins for euros with exchange rate is 1:1, but you can not buy Bytelandian coins. You have one Bytelandian gold coin. What is the maximum amount of euros you can get for it?
Write a function maximumEuros that takes an integer written on a Bytelandian gold coin. The function must return the maximum number of euros you can make using the given gold coin.
>>> euros(12) 13 >>> euros(2) 2
If we write the Bytelandian currency as $$\mathscr{B}$$, then you can exchange $$\mathscr{B}12$$ into $$\mathscr{B}6$$, $$\mathscr{B}4$$ and $$\mathscr{B}3$$, and then change these into €6 + €4 + €3 = €13.
If you try changing the $$\mathscr{B}2$$ coin into three smaller coins, you will get $$\mathscr{B}1$$, $$\mathscr{B}0$$ and $$\mathscr{B}0$$, and later you can get no more than €1 out of them. It is better to just change the $$\mathscr{B}2$$ coin directly into €2.