$n$ odd composite number, at most $\frac{n-1}{4}$ integers $a$ such that $n$ is a strong pseudoprime with respect to $a$

Question

The problem I'm trying to solve is: Let $n$ be an odd composite number. Show there are at most $\frac{n-1}{4}$ integers $a$ such that $1 \leq a \leq n$ and $n$ is a strong pseudoprime with respect to $a$. I know that a composite number is a number with at least two prime factors. But I'm very confused with how I can prove $n$ passes the Miller-Rabin test with respect to $a$. For start I don't see what I know about the decomposition $n-1 = 2^st$ if $n$ is a composite number. So I don't see how I can check whether the Miller-Rabin test holds. Since $n$ is odd I know $n-1$ is even and thus $s \geq 1$. But what do I know about $t$? All help is very much appreciated!