{"problem":{"name":"Sum-Product Ratio","description":{"content":"You are given non-zero integers $x_1, \\ldots, x_N$. Find the minimum and maximum values of $\\dfrac{x_i+x_j+x_k}{x_ix_jx_k}$ for integers $i$, $j$, $k$ such that $1\\leq i < j < k\\leq N$.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc158_b"},"statements":[{"statement_type":"Markdown","content":"You are given non-zero integers $x_1, \\ldots, x_N$. Find the minimum and maximum values of $\\dfrac{x_i+x_j+x_k}{x_ix_jx_k}$ for integers $i$, $j$, $k$ such that $1\\leq i < j < k\\leq N$.\n\n## Constraints\n\n*   $3\\leq N\\leq 2\\times 10^5$\n*   $-10^6\\leq x_i \\leq 10^6$\n*   $x_i\\neq 0$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$x_1$ $\\ldots$ $x_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc158_b","tags":[],"sample_group":[["4\n-2 -4 4 5","\\-0.175000000000000\n-0.025000000000000\n\n$\\dfrac{x_i+x_j+x_k}{x_ix_jx_k}$ can take the following four values.\n\n*   $(i,j,k) = (1,2,3)$: $\\dfrac{(-2) + (-4) + 4}{(-2)\\cdot (-4)\\cdot 4} = -\\dfrac{1}{16}$.\n*   $(i,j,k) = (1,2,4)$: $\\dfrac{(-2) + (-4) + 5}{(-2)\\cdot (-4)\\cdot 5} = -\\dfrac{1}{40}$．\n*   $(i,j,k) = (1,3,4)$: $\\dfrac{(-2) + 4 + 5}{(-2)\\cdot 4\\cdot 5} = -\\dfrac{7}{40}$．\n*   $(i,j,k) = (2,3,4)$: $\\dfrac{(-4) + 4 + 5}{(-4)\\cdot 4\\cdot 5} = -\\dfrac{1}{16}$.\n\nAmong them, the minimum is $-\\dfrac{7}{40}$, and the maximum is $-\\dfrac{1}{40}$."],["4\n1 1 1 1","3.000000000000000\n3.000000000000000"],["5\n1 2 3 4 5","0.200000000000000\n1.000000000000000"]],"created_at":"2026-03-03 11:01:14"}}