In this problem, you're given a function f(x) = ax^2 + bx + c(x in [l, r]) and a simple polygon. And we need you to figure out the length of f(x) in this polygon.
There are several test cases and the cases end with EOF. For each case:
The first line contains six integers n (1 <= n <= 20000), a(a != 0), b, c, l and r, which are the total of the points of the polygon and the parameters of the function and these parameters are in the range [-20000, 20000].
The next n lines contains two integers x and y, which are the coordinate of the point and both of them are in the range[-10^9, 10^9]. We can ensure that there is a edge between i-th point and (i+1)-th point (1 <= i < n) and there is a edge between first point and n-th point.
For each case, output your answer, your answer should rounded to two decimal places.