{"trustable":true,"prependHtml":"\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eThe triangulation of the set of the points on the plane is the set of triangles, satisfying the following\nconditions:\u003cbr\u003e\n1. no triangle is degenerate;\u003cbr\u003e\n2. no two triangles have a common interior point (common border points are allowed);\u003cbr\u003e\n3. all vertices of each triangle are the points from the given set;\u003cbr\u003e\n4. each point within the convex hull of the given points belongs to some triangle;\u003cbr\u003e\n5. no point of the given set belongs to the interior of a triangle.\u003cbr\u003e\n\u003c/p\u003e\n\u003cp\u003eA set of triangles is called pretriangulation if it satisfies all these conditions except possibly the last. A\npretriangulation is called minimal if it contains minimal possible number of triangles among all pretriangulations\nof the given set.\nA triangulation is called consecutive if it can be obtained from some minimal pretriangulation by successively\napplying the following split operation: choose a point that belongs to the interior of some triangle\nand connect it to the vertices of this triangle, splitting it to three smaller ones.\nGiven the set of the points on the plane, no three of which are lying on the same line, find the number\nof its consecutive triangulations. Two triangulations are different if they are different as sets of fixed\ntriangles.\n\u003c/p\u003e\n\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e\u003c/p\u003e\n\u003cp\u003e\nThe first line of the input file contains n -- the number of points (3 \u0026lt;\u003d n \u0026lt;\u003d 50). The following n lines\ncontain two integer numbers each -- coordinates of the points (no coordinate exceeds 10000 by its absolute\nvalue).\n\u003c/p\u003e\n\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\u003c/p\u003e\n\u003cp\u003e\nOutput the number of different consecutive trianguations of the given points set.\n\u003c/p\u003e\n\u003cb\u003eSample Input:\u003c/b\u003e\u003cpre\u003e4\n0 0\n3 3\n3 0\n0 3\n4\n0 0\n3 3\n3 0\n2 1\n\u003c/pre\u003e\n\u003cb\u003eSample Output:\u003c/b\u003e\u003cpre\u003e2\n1\n\u003c/pre\u003e\n\n\u003cbr\u003e\n"}}]}