It is possible to write five as a sum in exactly six different ways:

~~~
4 + 1
3 + 2
3 + 1 + 1
2 + 2 + 1
2 + 1 + 1 + 1
1 + 1 + 1 + 1 + 1
~~~

How many different ways can one hundred be written as a sum of at least two positive integers?