{"raw_statement":[{"iden":"problem statement","content":"A set of points $U$ in the $xy$\\-plane is called **good** if no point in $U$ lies in the **interior** of the convex hull of $U$. Note that the empty set is considered good.\nYou are given $N$ distinct points $v_1, v_2, \\dots, v_N$ in the $xy$\\-plane. The coordinates of the point $v_i$ are $(x_i, y_i)$. No three distinct points are collinear.\nCount the number of subsets $S$ of $V = \\lbrace v_1, v_2, \\dots, v_N \\rbrace$ such that both $S$ and $V \\setminus S$ are good sets."},{"iden":"constraints","content":"*   All input values are integers.\n*   $1 \\le N \\le 40$\n*   $|x_i|,|y_i|\\le 10^6$\n*   $(x_i,y_i)\\neq (x_j,y_j)\\ (i\\neq j)$\n*   No three distinct points are collinear."},{"iden":"input","content":"The input is given in the following format:\n\n$N$\n$x_1$ $y_1$\n$x_2$ $y_2$\n$\\vdots$\n$x_N$ $y_N$"},{"iden":"sample input 1","content":"4\n0 0\n3 0\n0 3\n1 1"},{"iden":"sample output 1","content":"14\n\nExcept for $\\emptyset$ and $V$, all other sets $S$ satisfy the condition."},{"iden":"sample input 2","content":"8\n1 0\n2 0\n3 1\n3 2\n2 3\n1 3\n0 2\n0 1"},{"iden":"sample output 2","content":"256"},{"iden":"sample input 3","content":"10\n0 0\n1 1\n7 1\n1 7\n3 2\n2 3\n4 2\n2 4\n5 4\n4 5"},{"iden":"sample output 3","content":"0"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}