{"problem":{"name":"C. Vladik and fractions","description":{"content":"Vladik and Chloe decided to determine who of them is better at math. Vladik claimed that for any positive integer _n_ he can represent fraction as a sum of three distinct positive fractions in form . ","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF743C"},"statements":[{"statement_type":"Markdown","content":"Vladik and Chloe decided to determine who of them is better at math. Vladik claimed that for any positive integer _n_ he can represent fraction as a sum of three distinct positive fractions in form .\n\nHelp Vladik with that, i.e for a given _n_ find three distinct positive integers _x_, _y_ and _z_ such that . Because Chloe can't check Vladik's answer if the numbers are large, he asks you to print numbers not exceeding 109.\n\nIf there is no such answer, print _\\-1_.\n\n## Input\n\nThe single line contains single integer _n_ (1 ≤ _n_ ≤ 104).\n\n## Output\n\nIf the answer exists, print 3 distinct numbers _x_, _y_ and _z_ (1 ≤ _x_, _y_, _z_ ≤ 109, _x_ ≠ _y_, _x_ ≠ _z_, _y_ ≠ _z_). Otherwise print _\\-1_.\n\nIf there are multiple answers, print any of them.\n\n[samples]","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"Vladik 和 Chloe 决定谁更擅长数学。Vladik 声称，对于任意正整数 $n$，他都能将分数 $\\frac{2}{n}$ 表示为三个互不相同的正分数之和，形式为 $\\frac{1}{x} + \\frac{1}{y} + \\frac{1}{z}$。\n\n请帮助 Vladik，即对于给定的 $n$，找出三个互不相同的正整数 $x$、$y$ 和 $z$，使得 $\\frac{1}{x} + \\frac{1}{y} + \\frac{1}{z} = \\frac{2}{n}$。由于 Chloe 无法在数字过大时验证 Vladik 的答案，他要求你输出的数字不超过 $10^9$。\n\n如果不存在这样的答案，请输出 _-1_。\n\n单行包含一个整数 $n$（$1 ≤ n ≤ 10^4$）。\n\n如果存在答案，请输出 $3$ 个互不相同的数 $x$、$y$ 和 $z$（$1 ≤ x, y, z ≤ 10^9$，$x ≠ y$，$x ≠ z$，$y ≠ z$）。否则输出 _-1_。\n\n如果存在多个答案，输出任意一个即可。\n\n## Input\n\n单行包含一个整数 $n$（$1 ≤ n ≤ 10^4$）。\n\n## Output\n\n如果存在答案，请输出 $3$ 个互不相同的数 $x$、$y$ 和 $z$（$1 ≤ x, y, z ≤ 10^9$，$x ≠ y$，$x ≠ z$，$y ≠ z$）。否则输出 _-1_。如果存在多个答案，输出任意一个即可。\n\n[samples]","is_translate":true,"language":"Chinese"},{"statement_type":"Markdown","content":"Given:  \n- Integer $ n $, where $ 1 \\leq n \\leq 10^4 $.  \n\nFind:  \n- Three distinct positive integers $ x, y, z $, each $ \\leq 10^9 $, such that  \n  $$\n  \\frac{2}{n} = \\frac{1}{x} + \\frac{1}{y} + \\frac{1}{z}.\n  $$\n\nIf no such triple exists, output $-1$.","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF743C","tags":["brute force","constructive algorithms","math","number theory"],"sample_group":[["3","2 7 42"],["7","7 8 56"]],"created_at":"2026-03-03 11:00:39"}}