Solve the programming task below in a Python markdown code block.
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: n/2, n/3 and n/4.
But these numbers are all rounded down (the banks have to make a profit).

You can also sell Bytelandian coins for American dollars. The exchange
rate is 1:1. But you can not buy Bytelandian coins.

You have one gold coin. What is the maximum amount of American dollars
you can get for it?

------ Input Format ------ 

The input will contain several test cases (not more than 10). \
Each testcase is a single line with a number n, it is the number written on your coin.

------ Output Format ------ 

For each test case output a single line, containing the maximum amount of American dollars you can make.

------ Constraints ------ 

$0 ≤ n ≤ 10^{9}$

----- Sample Input 1 ------ 
12
2

----- Sample Output 1 ------ 
13
2

----- explanation 1 ------ 
Test case 1: You can change 12 into 6, 4 and 3, and then change these into $6+4+3 = 13$. \
Test case 2: If you try changing the coin 2 into 3 smaller coins, you will get 1, 0 and 0, and later you can get no more than $1$ out of them. \
It is better just to change the $2$ coin directly into $2$.