Connect Coordinate

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Recently a renowned scientist, Chef discovered a planet. Total trees on planet are $N$ and are denoted by $X$ and $Y$ coordinates. Chef defined strength of a tree of the planet as the number of distinct subsets of remaining trees whose [convex hull](https://en.wikipedia.org/wiki/Convex_hull) can enclose the tree completely and strictly inside it. More formally, let $S(x)$ be strength of tree $

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