Benjamin Forest VIII is a king of a country. One of his best friends Nod lives in a village far from his castle. Nod gets seriously sick and is on the verge of death. Benjamin orders his subordinate Red to bring good medicine for him as soon as possible. However, there is no road from the castle to the village. Therefore, Red needs to climb over mountains and across canyons to reach the village. He has decided to get to the village on the shortest path on a map, that is, he will move on the straight line between the castle and the village. Then his way can be considered as polyline with n points (x₁, y₁)... (x_n, y_n) as illustlated in the following figure.

Here, x_i and y_i are coordinates of point i. The castle is located on the point (x₁, y₁), and the village is located on the point (x_n, y_n). Red can walk with speed v_w. Also, since he has a skill to cut a tunnel through a mountain horizontally, he can move strictly inside the mountain with speed v_c. Your job is to write a program to find the minimum time to get to the village.
The input is given in the following format: n v_w v_c x₁ y₁ ... x_n y_n You may assume all the following: 1 ≤ n ≤ 1000, 1 ≤ v_w, v_c ≤ 10, -10000 ≤ x_i, y_i ≤ 10000, and x_i < x_j for all i < j.
You should print the minimum time required to get to the village in a line. Each minimum time should be given as a decimal with an arbitrary number of fractional digits and with an absolute error of at most 10^-6.

sample input	sample output
3 2 1 0 0 50 50 100 0	70.710678

sample input	sample output
3 1 1 0 0 50 50 100 0	100.000000

sample input	sample output
3 1 2 0 0 50 50 100 0	50.000000

sample input	sample output
3 2 1 0 0 100 100 150 50	106.066017

sample input	sample output
6 1 2 0 0 50 50 100 0 150 0 200 50 250 0	150.000000

sample input	sample output
2 1 2 0 0 100 0	100.000000