I. DJ Mr. Spin
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

OC once took notice of a game called Reteeee. The core element of this game is spinning, which aroused his curiosity. To simplify, the game can be described as follows:

Assume there exists a rectangular plane coordinate system with the origin at $$$(0, 0)$$$. On this plane, there is a circle of radius $$$r$$$, centered at the origin. Inside the circle, there are $$$n$$$ distinct points $$$(x_i, y_i)$$$. You will have a point $$$P$$$ placed at the origin initially.

At the beginning of the game, the circle starts spinning counterclockwise at a speed of $$$v_1$$$ radians per second, and the points inside the circle spin along with it (around the center of the circle, at the same speed).

At time $$$t$$$, $$$P$$$ starts moving towards the positive X-axis at a speed of $$$v_2$$$ units per second. If vector $$$OP$$$ intersects a point, the point will disappear, and you will get $$$1$$$ point. The game ends as soon as $$$P$$$ intersects the circle.

Your task is to determine the minimum $$$t$$$ to achieve the maximum score.

Input

The first line contains three floating-point numbers $$$r, v_1, v_2$$$ $$$(1 \leq r, v_1, v_2 \leq 2 \times 10^5)$$$, denoting the radius of the circle, and the speed of the circle and $$$P$$$ respectively.

The second line contains one integer $$$n$$$ $$$(1 \leq n \leq 10^5)$$$, denoting the number of points.

For the following $$$n$$$ lines, the $$$i$$$-th line contains two integers $$$x_i, y_i$$$ $$$(0 \lt x_i^2 + y_i^2 \lt r^2)$$$, denoting the $$$i$$$-th point inside the circle.

It's guaranteed that $$$\frac{2 \pi}{v_1} \gt \frac{r}{v_2}$$$, and the points are distinct.

It's also guaranteed that the decimal places of the floating-point numbers do not exceed $$$3$$$.

Output

Output one line containing one floating-point number $$$t$$$, denoting the minimum time for $$$P$$$ to start moving and achieve the maximum score.

Your answer will be accepted if the absolute error between your answer and the standard answer does not exceed $$$10^{-3}$$$.

Examples
Input
4 3.141 2
3
0 -1
-2 0
0 3
Output
0.000
Input
5 3.141 2.828
5
2 -2
-3 -3
1 1
1 -4
-3 3
Output
0.654
Note

For the first example, $$$t = 0.000$$$. Here, $$$v_1$$$ is treated as $$$\pi$$$ (approximated). Let's simulate this according to the degree the circle has spun:

  1. $$$0^{\circ}$$$, $$$P$$$ starts moving, $$$A(0, -1), B(-2, 0), C(0, 3), P(0, 0)$$$.
    $$$0^{\circ}$$$$$$90^{\circ}$$$
  2. $$$90^{\circ}$$$, $$$A(1, 0), B(0, -2), C(-3, 0), P(1, 0)$$$. Vector $$$OP$$$ intersects point $$$A$$$, $$$A$$$ disappears, and you get $$$1$$$ point.
  3. $$$180^{\circ}$$$, $$$B(2, 0), C(0, -3), P(2, 0)$$$. Vector $$$OP$$$ intersects point $$$B$$$, $$$B$$$ disappears, and you get $$$1$$$ point.
    $$$180^{\circ}$$$$$$270^{\circ}$$$
  4. $$$270^{\circ}$$$, $$$C(3, 0), P(3, 0)$$$. Vector $$$OP$$$ intersects point $$$C$$$, $$$C$$$ disappears, and you get $$$1$$$ point.
  5. $$$360^{\circ}$$$, $$$P(4, 0)$$$. Vector $$$OP$$$ intersects the circle, the game ends.

For the second example, the optimal choice is to start moving when it will finally intersect the $$$4$$$-th point $$$(1, -4)$$$ and the circle at the same time.