Optimistan is a strange country. It is situated on an island
with a huge desert in the middle, so most people live in port
towns along the coast. As the name suggests, people of
Optimistan (also called Optimists) like to optimise everything,
so they only built roads necessary to connect all port towns
together and not a single extra road. That means that there is
only one way to get from one port town to another without
visiting the same place twice.
The government installed multidirectional distance signs in
$1$kilometre intervals on
one side of the road, to provide important information to
drivers. Thus whenever you go from one port town to another,
you pass the first sign at the port town and then one each
kilometre. Every distance sign contains the shortest distances
to all port towns, each written on a separate small sign
directed towards the goal town.
The signs also serve another important function: to guide
drivers on intersections. This means that distance of each
intersection from every port town is an integer number of
kilometres.
You bought a tourist guide of Optimistan which does not have
a map of the country, but it contains a huge table with the
shortest distances between all pairs of port towns. You quickly
calculated the average shortest distance between all pairs of
port towns, but then you started wondering: if the signs also
contained shortest distances to all other signs, what would be
the average number written on a sign? Could this be calculated
just from the distance table in the tourist guide?
Input
The input consists of:

one line with an integer $n$ ($2 \le n \le 500$), the number of
ports;

$n1$ lines, the
$i$th of which
contains $ni$
integers. The $j$th
integer on the $i$th
line denotes the distance between port $i$ and port $i+j$ in kilometres. Each distance
is between $1$ and
$10^6$
(inclusive).
You can assume that the distances correspond to a road
network in which there is exactly one path between two port
towns that does not visit the same place twice. All roads can
be used in both directions.
Output
Output one line with the average distances in kilometres
between all pairs of distance signs in Optimistan. Your answer
should have an absolute or relative error of at most
$10^{9}$.
If it is impossible to determine the exact average of
distances between all pairs of distance signs in Optimistan,
output “impossible”.
Sample Input 1 
Sample Output 1 
3
4 4
2

2.13333333333333

Sample Input 2 
Sample Output 2 
4
2 2 2
2 2
2

1.6
