Once the machines take over, the denomination of every coin will be a power of two: 1-cent, 2-cent, 4-cent, 8-cent, 16-cent, etc. There will be no limit to how much a coin can be worth.
A set of coins makes change for n if the sum of the values of the coins is n. For example, the following sets make change for 7:
7 1-cent coins
5 1-cent, 1 2-cent coins
3 1-cent, 2 2-cent coins
3 1-cent, 1 4-cent coins
1 1-cent, 3 2-cent coins
1 1-cent, 1 2-cent, 1 4-cent coins
Thus, there are 6 ways to make change for 7. Write a function count_change that takes a positive integer n and returns the number of ways to make change for n using these coins of the future:
"""Return the number of ways to make change for amount.