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Let `p(n)` represent the number of different ways in which n coins can be separated into piles.
For example, five coins can be separated into piles in exactly seven different ways, so `p(5)=7`.
~~~
OOOOO
OOOO O
OOO OO
OOO O O
OO OO O
OO O O O
O O O O O
~~~
Find the least value of n for which p(n) is divisible by one million.