A $100$-digit number is formed by writing the first $54$ natural numbers one after the other as $12345678...525354$. Find the remainder when this number is divided by $8$.

If $n=1+x$, where $x$ is the product of four consecutive positive integers, then which of the following statements is/are true?

(i) $n$ is odd

(ii) $n$ is prime

(iii) $n$ is a perfect square