Runaway to a Shadow

Description:

Input:

In the first line of the input the four integers x₀, y₀, v, T (|x₀|, |y₀| ≤ 10⁹, 0 ≤ v, T ≤ 10⁹) are given — the cockroach initial position on the table in the Cartesian system at the moment 0, the cockroach's constant speed and the time in seconds Dima needs for aiming respectively.

In the next line the only number n (1 ≤ n ≤ 100 000) is given — the number of shadow circles casted by plates.

In the next n lines shadow circle description is given: the i^th of them consists of three integers x_i, y_i, r_i (|x_i|, |y_i| ≤ 10⁹, 0 ≤ r ≤ 10⁹) — the i^th shadow circle on-table position in the Cartesian system and its radius respectively.

Consider that the table is big enough for the cockroach not to run to the table edges and avoid Dima's precise strike.

Output:

Print the only real number p — the probability of that the cockroach will stay alive.

Your answer will be considered correct if its absolute or relative error does not exceed 10^- 4.

Sample Input:

0 0 1 1
3
1 1 1
-1 -1 1
-2 2 1

Sample Output:

0.50000000000

Sample Input:

0 0 1 0
1
1 0 1

Sample Output:

1.00000000000

Note:

The picture for the first sample is given below.

Red color stands for points which being chosen as the cockroach's running direction will cause him being killed, green color for those standing for survival directions. Please note that despite containing a circle centered in ( - 2, 2) a part of zone is colored red because the cockroach is not able to reach it in one second.