Implementing geometry!

Let $ABCD$ be a parallelogram where $AC>BD$ , and point $O$ be the point where $AC$ and $BD$ intersect. Now circle with the center $O$ with the radius $OA$ intersects with the continuation of lines $AB$ and $AD$ in the points $L$ and $G$ , respectively. Define the intersection of $LG$ and $BD$ as Z and the midpoint of $AZ$ as $Y$ . Circle with the center in $Y$ and the the radius of $AY$ has to contain at least $n$ points mentioned in the text. What is the value of $n$ ?