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You have been sunbathing on a sand beach, and now you want to take a bath. You touch the sand, but it burns! How can you minimize the total pain to reach the sea?

Assume a two-dimensional world.
The beach has length ℓ and width *w*.
Where *y* ≤ 0, there is sea.
Where 0 < *x* < ℓ and 0 < *y* < *w*, there is sand.
The rest is covered by grass.
You are at a position (*a*, *b*)
strictly inside the beach.
Walking a unit on the sand causes pain *s*.
Walking a unit on the grass causes pain *g*,
with *g* < *s*.

To the right we see an example with ℓ = *w* = 30,
*a* = 12 and *b* = 20.
The black dot shows the origin (0, 0).
The red dot shows your position.
If *s* = 3 and *g* = 2, the best path (in blue)
goes straight into the sea.
If *s* = 13 and *g* = 5, the best path (in pink)
goes first straight on the sand to the point (0, 15),
and then straight on the grass into the sea.

unit=0.07cm

(100,100) sand0.92 0.82 0.68 grass0.39 0.78 0.0 sea0.0 0.48 0.68

linecolor=sand (20,20)(20,80)(80,80)(80,20)

linecolor=grass (00,20)(20,20)(20,80)(80,80)(80,20)(100,20)(100,100)(0,100)(00,20)

linecolor=sea (00,00)(00,20)(100,20)(100,00)(00,00)

linestyle=solid linewidth=2pt linecolor=black fillcolor=black (19.5,20)2

linestyle=dashed linecolor=magenta ->(44,60)(19.5,40) ->(19.5,40)(19.5,20)

linestyle=dashed linewidth=1.5pt linecolor=blue ->(44,60)(44,20)

linestyle=solid linewidth=2pt linecolor=red fillcolor=red (44,60)2

linecolor=black (50,85)ℓ ->(47,85)(20,85) ->(53,85)(80,85)

(85,50)*w*
->(85,47)(85,20)
->(85,53)(85,80)

Given ℓ, *w*, *a*, *b*, *s* and *g*,
can you minimize the pain to reach the sea?

**Input**

Input consists of several cases,
each with ℓ, *w*, *a*, *b*, *s* and *g*.
They are strictly positive real numbers
with at most three digits after the decimal point.
Assume *a* < ℓ, *b* < *w*, and *g* < *s*.

**Output**

For every case, print the minimum total pain to reach the sea with three digits after the decimal point. The input cases have no precision issues.

Public test cases

**Input**

30 30 12 20 3 2 30 30 12 20 13 5 25.5 12.1 23.6 4.7 18.4 5.3

**Output**

60.000 244.000 58.388

Information

- Author
- Salvador Roura
- Language
- English
- Official solutions
- C++
- User solutions
- C++