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.

Sample Input 1

1
0 1 1

Sample Output 1

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.

Sample Input 2

2
2 3 2 4 5 3 3 4 2

Sample Output 2

0 1 0 1 0 1 1 1 0

Sample Input 3

2
0 0 0 0 0 0 0 0 0

Sample Output 3

0 0 0 0 0 0 0 0 0

见题面 Input 部分

见题面 Output 部分