\gdef\thisproblemauthor{Ivan Kazmenko}
\gdef\thisproblemdeveloper{Ivan Kazmenko}
\begin{problem}{Revolving Lasers}
{revolving-lasers.in}{revolving-lasers.out}
{2 seconds (\textsl{3 seconds for Java})}{256 mebibytes}{}

\parskip=1pt

In this problem, you have to move the robot around the plane so as to
evade lasers for an arbitrary amount of time.

There are $n$ lasers on the two-dimensional plane.
Each laser consists of a source installed at a point with even integer
coordinates, and an infinite straight laser beam starting at that point.
A laser number $i$ turns uniformly by $t_i$ degrees per second:
a \textit{negative} number means turning clockwise,
a \textit{positive} one means turning counter-clockwise.
Initially, all lasers are directed upwards, collinear to $Oy$ axis.
No two sources are installed at a common point.
Lasers do not interfere with each other, so that the beams and sources
do not prevent propagation of other beams.

We control a robot which is initially located at the origin.
During each second, the robot either stays still or moves uniformly
and rectilinearly towards one of the eight neighbor points with integer
coordinates.
Two distinct points with integer coordinates $(x_1, y_1)$ and $(x_2, y_2)$
are considered neighbors if both their coordinates differ by at most one:
$|x_2 - x_1| \le 1$ and $|y_2 - y_1| \le 1$.

Your task is to construct a route such that the robot can move along
that route and evade the lasers for an arbitrary amount of time,
or determine that there is no such route.
Evading the lasers means that the robot can not be located on a laser source
and can not touch or cross a laser beam.
The sizes of objects and the thickness of the beam should be neglected.

\vskip -1pt
\InputFile
\vskip -1pt

The first line of input contains an integer $n$: the number of lasers
($0 \le n \le 3$). % Div1
% ($0 \le n \le 2$). % Div2
The next $n$ lines contain descriptions of lasers, one per line.
Each laser $i$ is defined by three space-separated integers
$x_i$, $y_i$ and $t_i$: the coordinates of the laser source
and the turning speed in degrees per second
($2 \le x_i, y_i \le 10$, $x_i$ and $y_i$ are even, % Div1
$-3 \le t_i \le 3$). % Div1
% ($2 \le x_i, y_i \le 10$, $x_i$ and $y_i$ are even, % Div2
% $-1 \le t_i \le 1$). % Div2
It is guaranteed that no two laser sources coincide.

\vskip -1pt
\OutputFile
\vskip -1pt

Print a non-empty string $S$ consisting of no more than $10\,000$ characters
which corresponds to the route you found.
Each character $S_i$ of the string specifies the action of the robot
during $i$-th second.
After performing all actions in the route, the positions of lasers and
the robot must correspond to their initial positions.
The characters used to encode the direction of movement correspond
to the positions of arrows on a numeric keypad:
when the robot is at point $(x, y$), \\
digits
\begin{tabular}{|c|c|c|}
\hline
\texttt{7} & \texttt{8} & \texttt{9} \\
\hline
\texttt{4} & \texttt{5} & \texttt{6} \\
\hline
\texttt{1} & \texttt{2} & \texttt{3} \\
\hline
\end{tabular}
mean moving to points
\begin{tabular}{|c|c|c|}
\hline
$(x - 1, y + 1)$ &
$(x, y + 1)$ &
$(x + 1, y + 1)$ \\
\hline
$(x - 1, y)$ &
$(x, y)$ &
$(x + 1, y)$ \\
\hline
$(x - 1, y - 1)$ &
$(x, y - 1)$ &
$(x + 1, y - 1)$ \\
\hline
\end{tabular}
.

If there are several possible answers, print any one of them.
If it is impossible to evade the lasers for an arbitrary amount of time,
print the word ``\texttt{None}'' instead of a route.

\vskip -1pt
\Examples

\exmpwidinf=0.23\thelinewidth
\exmpwidouf=0.63\thelinewidth
\begin{example}
\exmp{
1
2 2 1
}{
69\textit{555..(177)..55}9\textit{555..(89)..55}75112\textit{555..(86)..55}
}%
\exmp{
2
2 2 1
4 2 -1
}{
None
}%
\end{example}

\Explanations
\vskip -1pt

In the first example, the route consisting of $360$ steps is shortened
for readability: the fragments of the form ``\textit{ddd..($X$)..dd}''
mean repeating the digit \textit{d} exactly $X$ times.
The robot walks around the single laser source
in counter-clockwise direction and returns to the origin.

In the second example, it is impossible to evade the lasers
for an arbitrary amount of time.

\end{problem}
