\problemname{Island Tour}

\illustration{0.35}{iceland.jpg}{\href{https://www.publicdomainpictures.net/en/view-image.php?image=122025}{Iceland} by Irena Jackson, CC0 Public Domain}%
Tijmen, Annemarie and Imme are visiting Iceland, a beautiful island country
located in the middle of the Atlantic Ocean. To see as much of the island as
possible, they would like to visit all of the tourist attractions on the Ring
Road; the main road that runs around the circular perimeter of the island.
There are $n$ attractions, conveniently numbered from $1$ to $n$ in the order
they appear along the road.

Unfortunately, current distancing measures only allow one visitor at a time at any
given attraction, so they have decided to split up. Each person will start at a
different attraction, visiting the remaining attractions in circular order
around the Ring Road, i.e.\ a person starting their tour at attraction $i$
visits the attractions in the order $i$, $i+1$, $\ldots$, $n$, $1$, $\ldots$,
$i-1$.

They know how long it takes to travel from one attraction to the next and how
much time each person is going to spend at each attraction. They will each
start their tour at the same time and---due to their impatience---will follow
their plan without any waiting. Help Tijmen, Annemarie and Imme decide where
each person should start their tour such that there never comes a time where more
than one person is located at the same attraction. A person may enter an
attraction at the same moment another person leaves the attraction, and when a
person is finished visiting their last attraction they will immediately leave
the attraction and return to their hotel.

\begin{Input}
The input consists of:
\begin{itemize}
  \item One line with an integer $n$ ($1 \le n  \le 400$), the number of tourist attractions.
  \item One line with $n$ integers $d_1,\ldots,d_n$ ($1 \le d_i \le 10^6$ for
      each $i$), where $d_i$ is the travel time in minutes from tourist attraction
        $i$ to $i+1$ (or to $1$ when $i = n$).
  \item For each of Tijmen, Annemarie and Imme:
      \begin{itemize}
          \item One line with $n$ integers $t_{1}, \ldots, t_{n}$ ($1 \le t_{i}
              \le 10^6$ for each $i$), where $t_i$ is the time in minutes that the given
              person is going to spend at attraction $i$.
      \end{itemize}
\end{itemize}
\end{Input}

\begin{Output}
If there is a valid assignment, output one line with three integers, the
starting attraction for each person.  Otherwise, output
``\texttt{impossible}''. If there are multiple valid solutions, you may
output any one of them.
\end{Output}
