{"problem":{"name":"Triangle?","description":{"content":"In the $xy$\\-plane, we have $N$ points numbered $1$ through $N$.   Point $i$ is at the coordinates $(X_i,Y_i)$. Any two different points are at different positions.   Find the number of ways to choose","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc224_c"},"statements":[{"statement_type":"Markdown","content":"In the $xy$\\-plane, we have $N$ points numbered $1$ through $N$.  \nPoint $i$ is at the coordinates $(X_i,Y_i)$. Any two different points are at different positions.  \nFind the number of ways to choose three of these $N$ points so that connecting the chosen points with segments results in a triangle with a positive area.\n\n## Constraints\n\n*   All values in input are integers.\n*   $3 \\le N \\le 300$\n*   $-10^9 \\le X_i,Y_i \\le 10^9$\n*   $(X_i,Y_i) \\neq (X_j,Y_j)$ if $i \\neq j$.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$X_1$ $Y_1$\n$X_2$ $Y_2$\n$\\dots$\n$X_N$ $Y_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc224_c","tags":[],"sample_group":[["4\n0 1\n1 3\n1 1\n-1 -1","3\n\nThe figure below illustrates the points.\n![image](https://img.atcoder.jp/ghi/11f8cb446cb2872c9a712c59195a1268.png)\nThere are three ways to choose points that form a triangle: ${1,2,3},{1,3,4},{2,3,4}$."],["20\n224 433\n987654321 987654321\n2 0\n6 4\n314159265 358979323\n0 0\n-123456789 123456789\n-1000000000 1000000000\n124 233\n9 -6\n-4 0\n9 5\n-7 3\n333333333 -333333333\n-9 -1\n7 -10\n-1 5\n324 633\n1000000000 -1000000000\n20 0","1124"]],"created_at":"2026-03-03 11:01:13"}}