{"problem":{"name":"Three Sequences","description":{"content":"You are given a triple of positive integers $(X,Y,Z)$ such that $X\\leq Y\\leq Z$. Output one triple of sequences of non-negative integers $(S_1,S_2,S_3)$ that satisfies all of the following conditions:","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc211_b"},"statements":[{"statement_type":"Markdown","content":"You are given a triple of positive integers $(X,Y,Z)$ such that $X\\leq Y\\leq Z$.\nOutput one triple of sequences of non-negative integers $(S_1,S_2,S_3)$ that satisfies all of the following conditions:\n\n*   The lengths of $S_1,S_2,S_3$ are each between $1$ and $1000$, inclusive.\n*   The length of a longest sequence that is both a contiguous subsequence of $S_1$ and a contiguous subsequence of $S_2$ is $X$.\n*   The length of a longest sequence that is both a contiguous subsequence of $S_1$ and a contiguous subsequence of $S_3$ is $Y$.\n*   The length of a longest sequence that is both a contiguous subsequence of $S_2$ and a contiguous subsequence of $S_3$ is $Z$.\n*   $\\max(\\max(S_1),\\max(S_2),\\max(S_3))$ is minimized among all triples satisfying the above four conditions.\n\nIt can be proved that under the constraints of this problem, a triple $(S_1,S_2,S_3)$ satisfying the conditions always exists. If there are multiple such triples, you may output any of them.\n\n## Constraints\n\n*   $1\\leq X\\leq Y\\leq Z\\leq 100$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$X$ $Y$ $Z$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc211_b","tags":[],"sample_group":[["4 5 5","10 1 1 0 0 1 0 1 0 1 1\n8 1 1 0 1 0 0 1 1\n11 1 0 0 0 1 1 0 1 0 1 0\n\nIt can be verified that $S_1=(1,1,0,0,1,0,1,0,1,1),S_2=(1,1,0,1,0,0,1,1),S_3=(1,0,0,0,1,1,0,1,0,1,0)$ satisfies the conditions as follows:\n\n*   The lengths of $S_1,S_2,S_3$ are $10,8,11$, respectively, all of which are between $1$ and $1000$, inclusive.\n*   The longest sequences that are both a contiguous subsequence of $S_1$ and a contiguous subsequence of $S_2$ are $(1,0,0,1)$ and $(1,0,1,0)$, with length $X=4$.\n*   The longest sequences that are both a contiguous subsequence of $S_1$ and a contiguous subsequence of $S_3$ are $(1,0,1,0,1)$ and $(0,1,0,1,0)$, with length $Y=5$.\n*   The longest sequence that is both a contiguous subsequence of $S_2$ and a contiguous subsequence of $S_3$ is $(1,1,0,1,0)$, with length $Z=5$.\n*   $\\max(\\max(S_1),\\max(S_2),\\max(S_3))=1$, and it can be shown that it is impossible to satisfy the above four conditions with $\\max(\\max(S_1),\\max(S_2),\\max(S_3))=0$, so this is minimal."]],"created_at":"2026-03-03 11:01:14"}}