When flying between two places, constructing a good flight
plan is important. In general there is a wide range of
different factors to consider, the most important being fuel
consumption and weather forecasts (especially winds). In this
problem, we will evaluate flight plans with respect to a third
statistic, namely how much of the flight is over water, and how
much is over ground. This statistic is not relevant per se, yet
many passengers seem to prefer flying over land – either
because they are afraid of flying over water, or simply because
the view tends to be slightly more interesting when flying over
land.
For this problem, we assume that the earth is a perfect
sphere with radius $6370$
km. We model each continent of the earth as a polygon on this
sphere – a closed sequence of line segments, where a line
segment between two points consists of the shortest spherical
arc between these two points. The two endpoints of a line
segment can not be the same point, or antipodal (diametrically
opposite) points. Similarly a flight route is modeled as a
sequence of waypoints connected by line segments, but unlike
the line segments of a polygon these line segments may cross
themselves and will not necessarily end up where they
started.
In order to simplify the problem, we additionally make the
following two assumptions:
All coordinates on the sphere are represented as a pair of
latitude and longitude (both in degrees). A point with latitude
$\pm 90$ is the
north/south pole, and points with latitude $0$ are the points on the equator.
Input
The input consists of:

one line with an integer $1 \le c \le 30$, the number of
continents;

$c$ lines, each
describing a continent. Each such line starts with an
integer $3 \le n \le
30$, the number of vertices in the polygon
describing the continent. This is followed by $n$ pairs of integers $\phi _1, \lambda _1, \ldots , \phi _ n,
\lambda _ n$, where $90 \le \phi _ i \le 90$ and
$0 \le \lambda _ i \le
359$ are the latitude and longitude of the
$i$th vertex of the
continent;

one line describing the flight plan. The line starts
with an integer $2 \le m \le
30$, the number of waypoints. This is followed by
$m$ pairs of integers
$\phi _1, \lambda _1, \ldots
, \phi _ m, \lambda _ m$, where $90 \le \phi _ i \le 90$ and
$0 \le \lambda _ i \le
359$ are the latitude and longitude of the
$i$th waypoint of the
route.
A continent cannot cross itself. No continent will touch or
contain any other continent. Continents are given in
counterclockwise order, in the sense that if you go from the
first vertex of the polygon to the second one, the interior of
the continent is on your left hand side.
The first and last waypoints of the route will always be
inside a continent (but not necessarily the same
continent).
Output
Output two real numbers $l$ and $w$, where $l$ is the total length of the flight
(in km), and $w$ is the
percentage of the flight that is over water. The numbers should
be accurate to an absolute or relative error of at most
$10^{6}$.
Sample Input 1 
Sample Output 1 
1
4 45 0 45 0 45 90 45 90
5 0 180 0 359 0 160 0 170 0 180

40023.890406734 25.0000000000

Sample Input 2 
Sample Output 2 
2
6 62 80 28 49 10 80 37 95 8 134 51 129
3 52 188 29 165 24 188
4 19 77 33 180 69 169 29 75

21243.902224493 52.066390024
