Math Problem

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

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Description

Here has an function:
  $f(x) = |a * x^3 + b * x^2 + c * x + d| (L \leq x \leq R)$
Please figure out the maximum result of f(x).

Input

Multiple test cases(less than 100). For each test case, there will be only 1 line contains 6 numbers a, b, c, d, L and R. $(-10 \leq a, b, c, d \leq 10, -100 \leq L \leq R \leq 100)$

Output

For each test case, print the answer that was rounded to 2 digits after decimal point in 1 line.

Sample Input

1.00 2.00 3.00 4.00 5.00 6.00

Sample Output

310.00

Hint

heyang

Source

BestCoder Round #18

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