![(FRA 3)](/media/m/b/5/9/b5937f08a636dea93e54665919b340f4.png)
A polygon (not necessarily convex) with vertices in the lattice points of a rectangular grid is given. The area of the polygon is
![S.](/media/m/3/7/7/3772accbdc4fffed2efa17d53f141907.png)
If
![I](/media/m/3/8/6/38689d6affa9ba35368ca4d3d76ea147.png)
is the number of lattice points that are strictly in the interior of the polygon and B the number of lattice points on the border of the polygon, find the number
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$(FRA 3)$ A polygon (not necessarily convex) with vertices in the lattice points of a rectangular grid is given. The area of the polygon is $S.$ If $I$ is the number of lattice points that are strictly in the interior of the polygon and B the number of lattice points on the border of the polygon, find the number $T = 2S- B -2I + 2.$