Let $N$ be a positive multiple of $5$. One red ball and $N$ green balls are arranged in a line in random order. Let $P(N)$ be the probability that at least $\tfrac{3}{5}$ of the green balls are on the same side of the red ball. Observe that $P(5)=1$ and that $P(N)$ approaches $\tfrac{4}{5}$ as $N$ grows large. Find the sum of the digits of the least value of $N$ such that $P(N) < \tfrac{321}{400}$.

Let's think step by step and output the final answer within \boxed{}.
user