One famous Russian architect plans to build
a new monumental construction. It will be
a huge clock that indicates the time from
the beginning of the universe.

The face of this clock contains hands, moving
at constant speeds. They are numbered
from 1 to n from the fastest to the slowest one.
The fastest hand makes
one revolution per minute (60 seconds). Each next hand moves
slower than previous, the (i+1)-th hand makes one revolution
when the i-th hand makes d_{i} revolutions.
The setting mechanism of this clock is
very simple. You can take a hand by the handle,
located on its end, and move it in any direction.
When you move the hand, slower hands are moving
in proportion to their usual speeds, and faster
hands are not moving. Remember that hands are huge,
so setting this clock is a hard job.
Consider an example with three hands: a second hand,
a minute hand, and an hour hand. Their lengths are
5, 15 and 10 meters respectively. You want to set
the clock from 2:30 to 6:00 (fig.1). The easiest way to do it
is to rotate the minute hand 180^{∘} clockwise,
and then move the hour hand 90^{∘} clockwise.
The total distance you moved the handles of the hands
is approximately 62.83 meters.
Your task is to write a program that finds the way
to set the clock that minimizes the total distance
you have to move the handles.

Input file format

The first line of the input file contains one integer n — the number of
hands. The second line contains n−1 integer numbers
d_{1}, d_{2}, …, d_{n−1}. The third line
contains n integer numbers l_{1}, l_{2}, …, l_{n} —
lengths of clock hands.
Next two lines contain two non-negative integer numbers (one number per line): time indicated by
the clock and the actual time that should be set. Both times are measured in
seconds from the beginning of the universe and are less than 2^{63}.

Output file format

Print the minimal possible total distance
you have to move the handles. The answer must be precise to
at least 4 digits after decimal point.