{"raw_statement":[{"iden":"problem statement","content":"You are given a positive integer $N$. Print an integer sequence of length $L \\coloneqq N(N+1)/2$, $A = (A_1, A_2, \\ldots, A_L)$, that satisfies all of the following conditions.\n\n*   $A$ contains exactly $i$ occurrences of $i$ for every $i = 1, 2, \\ldots, N$.\n*   $1 \\leq |A_i - A_{i+1}| \\leq 2$ for every $i = 1, 2, \\ldots, L$. Here, $A_{L+1}$ means $A_1$.\n\nIt can be proved that, under the Constraints of this problem, there is always an integer sequence $A$ of length $L$ that satisfies all of the above conditions."},{"iden":"constraints","content":"*   $3 \\leq N \\leq 1000$\n*   $N$ is an integer."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"4"},{"iden":"sample output 1","content":"1 3 4 2 4 3 4 2 4 3\n\nThe integer sequence $A = (1, 3, 4, 2, 4, 3, 4, 2, 4, 3)$ contains exactly one $1$, two $2$s, three $3$s, and four $4$s, satisfying the first condition. The second condition is also satisfied, as follows:\n\n*   $|A_1 - A_2| = |1 - 3| = 2$\n*   $|A_2 - A_3| = |3 - 4| = 1$\n*   $|A_3 - A_4| = |4 - 2| = 2$\n*   $|A_4 - A_5| = |2 - 4| = 2$\n*   $|A_5 - A_6| = |4 - 3| = 1$\n*   $|A_6 - A_7| = |3 - 4| = 1$\n*   $|A_7 - A_8| = |4 - 2| = 2$\n*   $|A_8 - A_9| = |2 - 4| = 2$\n*   $|A_9 - A_{10}| = |4 - 3| = 1$\n*   $|A_{10} - A_1| = |3 - 1| = 2$"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}