Problem Statement

There is zero or one bomb at each of positions $0, 1, 2, \ldots, 3^N-1$. Let us say that positions $x$ and $y$ are neighboring each other if and only if the following condition is satisfied for every $i=1, \ldots, N$.

• Let $x'$ and $y'$ be the $i$-th lowest digits of $x$ and $y$ in ternary representation, respectively. Then, $|x' - y'| \leq 1$.

It 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.

Constraints

• $1 \leq N \leq 12$
• There is a placement of bombs consistent with $A_0, A_1, \ldots, A_{3^N-1}$.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N
A_0 A_1 \ldots A_{3^N-1}

Output

Print $B_0, B_1, \ldots, B_{3^N-1}$ with spaces in between, where $B_i = 0$ if position $i$ has no bomb and $B_i = 1$ if position $i$ has a bomb.