On the beach

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?

0.53 Assume a two-dimensional world. The beach has length $\ell$ and width $w$ . Where $y \le 0$ , there is sea. Where $0 < x < \ell$ 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 $\ell = w = 30$ , $a = 12$ 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.

0.50

(100,100)

(20,20)(20,80)(80,80)(80,20)

(00,20)(20,20)(20,80)(80,80)(80,20)(100,20)(100,100)(0,100)(00,20)

(00,00)(00,20)(100,20)(100,00)(00,00)

(19.5,20)2

(44,60)(19.5,40) (19.5,40)(19.5,20)

(44,60)(44,20)

(44,60)2

(50,85) $\ell$ (47,85)(20,85) (53,85)(80,85)

(85,50) $w$ (85,47)(85,20) (85,53)(85,80)

Given $\ell$ , $w$ , $a$ , $b$ , $s$ and $g$ , can you minimize the pain to reach the sea?

Input

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

Problem information

Author: Salvador Roura

Generation: 2026-01-25T12:06:50.831Z