ITMC 2026 Grade 7 National Preliminary sample-r1 Question 24

For a positive integer $n$, let $P(n)$ be the product of its digits and $S(n)$ their sum. For example, $P(29)=2\cdot9=18$ and $S(29)=2+9=11$.

$N$ is the smallest positive integer with $P(N)=2560$. Find $S(N)$.