Find the number of integers n such that 1 <= n <= 1000 and n is a multiple of 7 but not a multiple of 2 or 3.

The problem asks us to find the number of integers $n$ such that $1 \le n \le 1000$ and $n$ is a multiple of 7 but not a multiple of 2 or 3.

Let $S = \{1, 2, \dots, 1000\}$.
Let $A$ be the set of integers in $S$ that are multiples of 7.
Let $B$ be the set of integers in $S$ that are multiples of 2.
Let $C$ be the set of integers in $S$ that are multiples of 3.

We are looking for the number of integers $n$ such that $n \in A$ and $n \notin B$ and $