Problem A
Amalgamated Artichokes

Picture by Hans Hillewaert via Wikimedia Commons

Fatima has done some previous analyses and has found that the stock price over any period of time can be modelled reasonably accurately with the following equation:

where $p$, $a$, $b$, $c$ and $d$ are constants. Fatima would like you to write a program to determine the largest price decline over a given sequence of prices. Figure 1 illustrates the price function for Sample Input 1. You have to consider the prices only for integer values of $k$.

Figure 1: Sample Input 1. The largest decline occurs from the fourth to the seventh price.

Input

The input consists of a single line containing $6$ integers $p$ ($1\le p\le 1000$), $a$, $b$, $c$, $d$ ($0\le a,b,c,d\le 1000$) and $n$ ($1\le n\le {10}^6$). The first $5$ integers are described above. The sequence of stock prices to consider is $\mathrm{price}(1),\mathrm{price}(2),\dots ,\mathrm{price}(n)$.

Output

Display the maximum decline in the stock prices. If there is no decline, display the number $0$. Your output should have an absolute or relative error of at most ${10}^{-6}$.

42 1 23 4 8 10

104.855110477

100 7 615 998 801 3

0.00

100 432 406 867 60 1000

399.303813