Migrated from Lutece 804 Lovely Calculus

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Description

Parabola is very important in math, I believe every one of you should be very familiar with that.

A parabola on a $XOY$ plane can be expressed as $y = ax^2 + bx + c$ ($a\neq 0$) (Well, you can see we have simplified the problem a little bit...)

In this problem, a point $(x_{i}, y_{i})$ is said to be "inside a parabola", if such conditions holds:

If $a > 0$, then $y_{i}\geq ax_{i}^2 + bx_{i} + c$.

If $a < 0$, then $y_{i}\leq ax_{i}^2 + bx_{i} + c$.

Given two parabolas, one with $a > 0$, the other with $a < 0$, you need to find the intersection of two parabolas. Which is the area made up by all the points $(x_{i}, y_{i})$ which are inside both parabolas.

Input

The test contains two lines, the first line with three numbers $a_{1}, b_{1}, c_{1}$, given a parabola $y = a_{1}x^2 + b_{1}x + c_{1}$.

The second line comes three numbers $a_{2}, b_{2}, c_{2}$, given a parabola $y = a_{2}x^2 + b_{2}x + c_{2}$

$-100\leq a_{1}, b_{1}, c_{1}, a_{2}, b_{2}, c_{2}\leq 100, a_{1}a_{2} < 0$.

Output

Output the area of intersection, rounded to $3$ digits after decimal point.

Samples

8 -10 3
-5 7 2

3.598

Note

You can use printf("%.3f\n") to output the answer

Resources

the 12th UESTC Programming Contest Preliminary