{"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\u003eEdward has \u003cvar\u003en\u003c/var\u003e points on the plane. He picks a subset of points (at least three points), and defines the beauty of the subset as twice the area of corresponding convex hull. Edward wants to know summation of the beauty of all possible subsets of points (at least three points).\u003c/p\u003e\n\n\u003cp\u003eNo two points coincide and no three points are on the same line.\u003c/p\u003e\n\n\u003ch4\u003eInput\u003c/h4\u003e\n\u003cp\u003eThere are multiple test cases. The first line of input contains an integer \u003cvar\u003eT\u003c/var\u003e indicating the number of test cases. For each test case:\u003c/p\u003e\n\n\u003cp\u003eThe first line contains an integer \u003cvar\u003en\u003c/var\u003e (3 ≤ \u003cvar\u003en\u003c/var\u003e ≤ 1000). Each of following \u003cvar\u003en\u003c/var\u003e lines contains 2 integers \u003cvar\u003ex\u003c/var\u003e\u003csub\u003e\u003cvar\u003ei\u003c/var\u003e\u003c/sub\u003e, \u003cvar\u003ey\u003c/var\u003e\u003csub\u003e\u003cvar\u003ei\u003c/var\u003e\u003c/sub\u003e which denotes a point (\u003cvar\u003ex\u003c/var\u003e\u003csub\u003e\u003cvar\u003ei\u003c/var\u003e\u003c/sub\u003e, \u003cvar\u003ey\u003c/var\u003e\u003csub\u003e\u003cvar\u003ei\u003c/var\u003e\u003c/sub\u003e) (0 ≤ |\u003cvar\u003ex\u003c/var\u003e\u003csub\u003e\u003cvar\u003ei\u003c/var\u003e\u003c/sub\u003e|, |\u003cvar\u003ey\u003c/var\u003e\u003csub\u003e\u003cvar\u003ei\u003c/var\u003e\u003c/sub\u003e| ≤ 10\u003csup\u003e9\u003c/sup\u003e). \u003c/p\u003e\u003cp\u003e\n\n\u003c/p\u003e\u003cp\u003eThe sum of values \u003cvar\u003en\u003c/var\u003e for all the test cases does not exceed 5000.\u003c/p\u003e\n\n\u003ch4\u003eOutput\u003c/h4\u003e\n\u003cp\u003eFor each case, if the answer is \u003cvar\u003eS\u003c/var\u003e, output a single integer denotes \u003cvar\u003eS\u003c/var\u003e modulo 998244353.\n\n\u003c/p\u003e\u003ch4\u003eSample\u003c/h4\u003e\n\u003ctable class\u003d\"vjudge_sample\"\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e1\n3\n0 0\n0 1\n1 0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\n"}}]}