{"problem":{"name":"Picking Up","description":{"content":"There are $N$ balls in a two-dimensional plane. The $i$\\-th ball is at coordinates $(x_i, y_i)$. We will collect all of these balls, by choosing two integers $p$ and $q$ such that $p \\neq 0$ or $q \\ne","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"diverta2019_2_b"},"statements":[{"statement_type":"Markdown","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 $q$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 50$\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.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$x_1$ $y_1$\n$:$\n$x_N$ $y_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"diverta2019_2_b","tags":[],"sample_group":[["2\n1 1\n2 2","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 $(1, 1)$, $(2, 2)$."],["3\n1 4\n4 6\n7 8","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 $(7, 8)$, $(4, 6)$, $(1, 4)$."],["4\n1 1\n1 2\n2 1\n2 2","2"]],"created_at":"2026-03-03 11:01:14"}}