Let $N$ be a positive multiple of 7. One red ball and $N$ green balls are arranged in a line in random order. Let $P(N)$ be the probability that at least $\frac{4}{7}$ of the green balls are on the same side of the red ball. Observe that $P(7)=1$ and that $P(N)$ approaches $\frac{6}{7}$ as $N$ grows large. What is the sum of the digits of the least value of $N$ such that $P(N)<\frac{43}{50}$?