A parabolic vertical crest curve connects two road segments with grades $+1.0 \%$ and $-2.0 \%.$ If a $200 \; \text{m}$ stopping sight distance is needed for a driver at a height of $1.2 \; \text{m}$ to avoid an obstacle of height $0.15 \; \text{m},$ then the minimum curve length should be _________ $\text{m}$. (round off to the nearest integer)