{"raw_statement":[{"iden":"problem statement","content":"We define sequences $S_n$ as follows.\n\n*   $S_1$ is a sequence of length $1$ containing a single $1$.\n*   $S_n$ ($n$ is an integer greater than or equal to $2$) is a sequence obtained by concatenating $S_{n-1}$, $n$, $S_{n-1}$ in this order.\n\nFor example, $S_2$ and $S_3$ is defined as follows.\n\n*   $S_2$ is a concatenation of $S_1$, $2$, and $S_1$, in this order, so it is $1,2,1$.\n*   $S_3$ is a concatenation of $S_2$, $3$, and $S_2$, in this order, so it is $1,2,1,3,1,2,1$.\n\nGiven $N$, print the entire sequence $S_N$."},{"iden":"constraints","content":"*   $N$ is an integer.\n*   $1 \\leq N \\leq 16$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"2"},{"iden":"sample output 1","content":"1 2 1\n\nAs described in the Problem Statement, $S_2$ is $1,2,1$."},{"iden":"sample input 2","content":"1"},{"iden":"sample output 2","content":"1"},{"iden":"sample input 3","content":"4"},{"iden":"sample output 3","content":"1 2 1 3 1 2 1 4 1 2 1 3 1 2 1\n\n*   $S_4$ is a concatenation of $S_3$, $4$, and $S_3$, in this order."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}