{"raw_statement":[{"iden":"problem statement","content":"There are $N$ balls in a two-dimensional plane. The $i$\\-th ball is at coordinates $(x_i, y_i)$.\nWe will collect all of these balls, by choosing two integers $p$ and $q$ such that $p \\neq 0$ or $q \\neq 0$ and then repeating the following operation:\n\n*   Choose a ball remaining in the plane and collect it. Let $(a, b)$ be the coordinates of this ball. If we collected a ball at coordinates $(a - p, b - q)$ in the previous operation, the cost of this operation is $0$. Otherwise, including when this is the first time to do this operation, the cost of this operation is $1$.\n\nFind the minimum total cost required to collect all the balls when we optimally choose $p$ and $q$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 50$\n*   $|x_i|, |y_i| \\leq 10^9$\n*   If $i \\neq j$, $x_i \\neq x_j$ or $y_i \\neq y_j$.\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$x_1$ $y_1$\n$:$\n$x_N$ $y_N$"},{"iden":"sample input 1","content":"2\n1 1\n2 2"},{"iden":"sample output 1","content":"1\n\nIf we choose $p = 1, q = 1$, we can collect all the balls at a cost of $1$ by collecting them in the order $(1, 1)$, $(2, 2)$."},{"iden":"sample input 2","content":"3\n1 4\n4 6\n7 8"},{"iden":"sample output 2","content":"1\n\nIf we choose $p = -3, q = -2$, we can collect all the balls at a cost of $1$ by collecting them in the order $(7, 8)$, $(4, 6)$, $(1, 4)$."},{"iden":"sample input 3","content":"4\n1 1\n1 2\n2 1\n2 2"},{"iden":"sample output 3","content":"2"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}