{"raw_statement":[{"iden":"problem statement","content":"There is zero or one bomb at each of positions $0, 1, 2, \\ldots, 3^N-1$.  \nLet us say that positions $x$ and $y$ are **neighboring** each other if and only if the following condition is satisfied for every $i=1, \\ldots, N$.\n\n*   Let $x'$ and $y'$ be the $i$\\-th lowest digits of $x$ and $y$ in ternary representation, respectively. Then, $|x' - y'| \\leq 1$.\n\nIt is known that there are exactly $A_i$ bombs in total at the positions neighboring position $i$. Print a placement of bombs consistent with this information."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 12$\n*   There is a placement of bombs consistent with $A_0, A_1, \\ldots, A_{3^N-1}$.\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$A_0$ $A_1$ $\\ldots$ $A_{3^N-1}$"},{"iden":"sample input 1","content":"1\n0 1 1"},{"iden":"sample output 1","content":"0 0 1\n\nPosition $0$ is neighboring positions $0$ and $1$, which have $0$ bombs in total.  \nPosition $1$ is neighboring positions $0$, $1$, and $2$, which have $1$ bomb in total.  \nPosition $2$ is neighboring positions $1$ and $2$, which have $1$ bombs in total.  \nIf there is a bomb at only position $2$, all conditions above are satisfied, so this placement is correct."},{"iden":"sample input 2","content":"2\n2 3 2 4 5 3 3 4 2"},{"iden":"sample output 2","content":"0 1 0 1 0 1 1 1 0"},{"iden":"sample input 3","content":"2\n0 0 0 0 0 0 0 0 0"},{"iden":"sample output 3","content":"0 0 0 0 0 0 0 0 0"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}