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Let $S$ be the set of all triangles in the $xy$-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in $S$ has area 50 sq. units, then the number of elements in the set $S$ is:
(1) $9$
(2) $18$
(3) $36$
(4) $32$
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