\Problem{Statisticians}{statisticians}
% author: Fredrik Svensson

\noindent
Statisticians like to create a lot of statistics. One simple measure
is the mean value: the sum of all values divided by the
number of values. Another is the median: the middle among all
values when they have been sorted. If there are an even number of
values, the mean of the two middle values will form the median.

These kinds of measures can be used for example to describe the
population in a country or even some parts of the population in the
country. Anne Jensen, Maria Virtanen, Jan Hansen, Erik Johansson and
Jón Ţórsson want to find a statistical measurement of how many
statisticians there are in the Nordic countries. To be more precise,
they want to find out how many statisticians there are per unit area.
As the population in the Nordic countries are well spread out they will
try the new measurement MAD, Median of All Densities. First put a
square grid on the map. Then draw a rectangle aligned with the grid
and calculate the density of statisticians in that area, i.e. the mean
number of statisticians per area unit. After that,
repeat the procedure until all possible rectangles have been covered.
Finally the MAD is the median of all statistician densities.

\Input
The first line of the input contains of two space separated numbers $h$
and $w$ describing the height and width of the square grid, where
$1 \leq h \leq 140$ and $1 \leq w \leq 120$. The next line contains
two space separated numbers $a$ and $b$ which are the lower and upper
bound of the allowed rectangle areas, i.e.
$1 \leq a \leq rectangle area \leq b \leq w \times h$.
Then there will follow $h$ lines with $w$ space separated numbers $s$
describing the number of statisticians in each square of the map,
$0 \leq s \leq 10000$. There will always exist a rectangle which area
is in $[a,b]$.

\Output
The output contains of one line with the MAD. The number should be
printed in number of statisticians per square and contain three
decimals. The absolute error must be $< 10^{-3}$.

\Xample{statisticians/statisticians.1}

\Xample{statisticians/statisticians.2}

