{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n section pre {\n display: block;\n padding: 9.5px;\n margin: 0 0 10px;\n font-size: 13px;\n line-height: 1.42857143;\n word-break: break-all;\n word-wrap: break-word;\n color: #333;\n background: rgba(255, 255, 255, 0.5);\n border: 1px solid #ccc;\n border-radius: 6px;\n }\n\u003c/style\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n {left: \u0027\\\\[\u0027, right: \u0027\\\\]\u0027, display: true}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"Problem Statement","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eIn the \u003cvar\u003e\\(xy\\)\u003c/var\u003e-plane, we have \u003cvar\u003e\\(N\\)\u003c/var\u003e points numbered \u003cvar\u003e\\(1\\)\u003c/var\u003e through \u003cvar\u003e\\(N\\)\u003c/var\u003e.\u003cbr\u003e\r\nPoint \u003cvar\u003e\\(i\\)\u003c/var\u003e is at the coordinates \u003cvar\u003e\\((X_i,Y_i)\\)\u003c/var\u003e. Any two different points are at different positions.\u003cbr\u003e\r\nFind the number of ways to choose three of these \u003cvar\u003e\\(N\\)\u003c/var\u003e points so that connecting the chosen points with segments results in a triangle with a positive area.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Constraints","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eAll values in input are integers.\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(3 \\le N \\le 300\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(-10^9 \\le X_i,Y_i \\le 10^9\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\((X_i,Y_i) \\neq (X_j,Y_j)\\)\u003c/var\u003e if \u003cvar\u003e\\(i \\neq j\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Input","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eInput is given from Standard Input in the following format:\u003c/p\u003e\r\n\u003cpre\u003e\u003cvar\u003e\\(N\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(X_1\\)\u003c/var\u003e \u003cvar\u003e\\(Y_1\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(X_2\\)\u003c/var\u003e \u003cvar\u003e\\(Y_2\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(\\dots\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(X_N\\)\u003c/var\u003e \u003cvar\u003e\\(Y_N\\)\u003c/var\u003e\r\n\u003c/pre\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Output","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003ePrint the answer as an integer.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 1","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\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\u003e4\r\n0 1\r\n1 3\r\n1 1\r\n-1 -1\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\u003cp\u003eThe figure below illustrates the points.\u003c/p\u003e\r\n\u003cp\u003e\u003cimg alt\u003d\"\" src\u003d\"CDN_BASE_URL/1b597e14a2c9124ea825b7f59276138d?v\u003d1715429832\"\u003e\u003c/p\u003e\r\n\u003cp\u003eThere are three ways to choose points that form a triangle: \u003cvar\u003e\\(\\{1,2,3\\},\\{1,3,4\\},\\{2,3,4\\}\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 2","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\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\u003e20\r\n224 433\r\n987654321 987654321\r\n2 0\r\n6 4\r\n314159265 358979323\r\n0 0\r\n-123456789 123456789\r\n-1000000000 1000000000\r\n124 233\r\n9 -6\r\n-4 0\r\n9 5\r\n-7 3\r\n333333333 -333333333\r\n-9 -1\r\n7 -10\r\n-1 5\r\n324 633\r\n1000000000 -1000000000\r\n20 0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1124\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\u003c/section\u003e\r\n"}}]}