I thought that there would be more....

Geometry Level 5

On the xy-plane consider a square grid with corners (0,0), (0,10), (10,10) and (10,0). Let S be the set of all (non-degenerate) triangles that can be formed with vertices that have integer coordinates on this grid. (For example, the triangle with vertices (0,1), (5,5) and (9,2) would be one element of S).

How many distinct area values are there among the elements of S?

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