{"raw_statement":[{"iden":"problem statement","content":"You are given an integer $N$. Determine if there exists a tuple of subsets of ${1,2,...N}$, $(S_1,S_2,...,S_k)$, that satisfies the following conditions:\n\n*   Each of the integers $1,2,...,N$ is contained in exactly two of the sets $S_1,S_2,...,S_k$.\n*   Any two of the sets $S_1,S_2,...,S_k$ have exactly one element in common.\n\nIf such a tuple exists, construct one such tuple."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^5$\n*   $N$ is an integer."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"3"},{"iden":"sample output 1","content":"Yes\n3\n2 1 2\n2 3 1\n2 2 3\n\nIt can be seen that $(S_1,S_2,S_3)=({1,2},{3,1},{2,3})$ satisfies the conditions."},{"iden":"sample input 2","content":"4"},{"iden":"sample output 2","content":"No"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}