{"raw_statement":[{"iden":"problem statement","content":"There are $N$ people in a three-dimensional space. The $i$\\-th person is at the coordinates $(X_i,Y_i,Z_i)$.  \nAll people are at different coordinates, and we have $X_i>0$ for every $i$.\nYou will choose a point $p=(x,y,z)$ such that $x<0$, and take a photo in the positive $x$\\-direction.\nIf the point $p$ and the positions $A, B$ of two people are on the same line in the order $p,A,B$, then the person at $B$ will not be in the photo. There are no other potential obstacles.\nFind the number of people in the photo when $p$ is chosen to minimize this number."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 50$\n*   $0 < X_i \\leq 1000$\n*   $-1000 \\leq Y_i,Z_i \\leq 1000$\n*   The triples $(X_i,Y_i,Z_i)$ are distinct.\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$X_1$ $Y_1$ $Z_1$\n$\\vdots$\n$X_N$ $Y_N$ $Z_N$"},{"iden":"sample input 1","content":"3\n1 1 1\n2 2 2\n100 99 98"},{"iden":"sample output 1","content":"2\n\nFor instance, if you take the photo from the point $(-0.5,-0.5,-0.5)$, it will not show the second person."},{"iden":"sample input 2","content":"8\n1 1 1\n1 1 -1\n1 -1 1\n1 -1 -1\n3 2 2\n3 2 -2\n3 -2 2\n3 -2 -2"},{"iden":"sample output 2","content":"4\n\nIf you take the photo from the point $(-1,0,0)$, it will show four people."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}