On the beach P94819

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

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.