### 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.

### 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.

### 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.

0 0 1

Position 0 is neighboring positions 0 and 1, which have 0 bombs in total.
Position 1 is neighboring positions 0, 1, and 2, which have 1 bomb in total.
Position 2 is neighboring positions 1 and 2, which have 1 bombs in total.
If there is a bomb at only position 2, all conditions above are satisfied, so this placement is correct.