{"problem":{"name":"B. Gluttony","description":{"content":"You are given an array _a_ with _n_ distinct integers. Construct an array _b_ by permuting _a_ such that for every non-empty subset of indices _S_ = {_x_1, _x_2, ..., _x__k_} (1 ≤ _x__i_ ≤ _n_, 0 < _k","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF891B"},"statements":[{"statement_type":"Markdown","content":"You are given an array _a_ with _n_ distinct integers. Construct an array _b_ by permuting _a_ such that for every non-empty subset of indices _S_ = {_x_1, _x_2, ..., _x__k_} (1 ≤ _x__i_ ≤ _n_, 0 < _k_ < _n_) the sums of elements on that positions in _a_ and _b_ are different, i. e.\n\n## Input\n\nThe first line contains one integer _n_ (1 ≤ _n_ ≤ 22) — the size of the array.\n\nThe second line contains _n_ space-separated distinct integers _a_1, _a_2, ..., _a__n_ (0 ≤ _a__i_ ≤ 109) — the elements of the array.\n\n## Output\n\nIf there is no such array _b_, print _\\-1_.\n\nOtherwise in the only line print _n_ space-separated integers _b_1, _b_2, ..., _b__n_. Note that _b_ must be a permutation of _a_.\n\nIf there are multiple answers, print any of them.\n\n[samples]\n\n## Note\n\nAn array _x_ is a permutation of _y_, if we can shuffle elements of _y_ such that it will coincide with _x_.\n\nNote that the empty subset and the subset containing all indices are not counted.","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"给你一个包含 $n$ 个互不相同整数的数组 $[a]$。请通过重排 $[a]$ 构造一个数组 $[b]$，使得对于每一个非空真子集的索引集合 $S = \\{x_1, x_2, \\dots, x_k\\}$（其中 $1 \\le x_i \\le n$，且 $0 < k < n$），在 $[a]$ 和 $[b]$ 中这些位置上的元素之和均不相等，即\n\n第一行包含一个整数 $n$（$1 \\le n \\le 22$）——数组的大小。\n\n第二行包含 $n$ 个空格分隔的互不相同的整数 $a_1, a_2, \\dots, a_n$（$0 \\le a_i \\le 10^9$）——数组的元素。\n\n如果不存在这样的数组 $[b]$，请输出 _-1_。\n\n否则，在唯一的一行中输出 $n$ 个空格分隔的整数 $b_1, b_2, \\dots, b_n$。注意 $[b]$ 必须是 $[a]$ 的一个排列。\n\n如果有多个答案，输出任意一个即可。\n\n数组 $[x]$ 是 $[y]$ 的一个排列，当且仅当我们可以对 $[y]$ 的元素重新排序使其与 $[x]$ 完全一致。\n\n注意：空子集和包含所有索引的子集不计入。\n\n## Input\n\n第一行包含一个整数 $n$（$1 \\le n \\le 22$）——数组的大小。第二行包含 $n$ 个空格分隔的互不相同的整数 $a_1, a_2, \\dots, a_n$（$0 \\le a_i \\le 10^9$）——数组的元素。\n\n## Output\n\n如果不存在这样的数组 $[b]$，请输出 _-1_。否则，在唯一的一行中输出 $n$ 个空格分隔的整数 $b_1, b_2, \\dots, b_n$。注意 $[b]$ 必须是 $[a]$ 的一个排列。如果有多个答案，输出任意一个即可。\n\n[samples]\n\n## Note\n\n数组 $[x]$ 是 $[y]$ 的一个排列，当且仅当我们可以对 $[y]$ 的元素重新排序使其与 $[x]$ 完全一致。注意：空子集和包含所有索引的子集不计入。","is_translate":true,"language":"Chinese"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ n \\in \\mathbb{Z} $, $ 1 \\leq n \\leq 22 $.  \nLet $ A = (a_1, a_2, \\dots, a_n) $ be a sequence of $ n $ distinct integers, $ 0 \\leq a_i \\leq 10^9 $.  \nLet $ B = (b_1, b_2, \\dots, b_n) $ be a permutation of $ A $.\n\n**Constraints**  \nFor every non-empty proper subset $ S \\subset \\{1, 2, \\dots, n\\} $, $ 0 < |S| < n $,  \n$$\n\\sum_{i \\in S} a_i \\ne \\sum_{i \\in S} b_i\n$$\n\n**Objective**  \nFind such a permutation $ B $ of $ A $, or output $-1$ if none exists.","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF891B","tags":["constructive algorithms","greedy"],"sample_group":[["2\n1 2","2 1"],["4\n1000 100 10 1","100 1 1000 10"]],"created_at":"2026-03-03 11:00:39"}}