There are $n$ members of Chennai Mathematical Institute. Most of them are very studious and like to own lots of books. Now the following facts have been learnt.
- No two members own exactly the same number of books.
- Each member owns strictly less than $n$ books.
- No member has exactly $200$ books.
Given the above information, which of the following is not a possible value of $n?$
-
$100$
-
$199$
-
$200$
-
$201$