4702: Runaway to a Shadow
内存限制：256 MB
时间限制：2 S
题面：传统
评测方式：文本比较
上传者：
提交：8
通过：1
题目描述
time limit per test
1 secondmemory limit per test
256 megabytesinput
standard inputoutput
standard outputDima is living in a dormitory, as well as some cockroaches.
At the moment 0 Dima saw a cockroach running on a table and decided to kill it. Dima needs exactly T seconds for aiming, and after that he will precisely strike the cockroach and finish it.
To survive the cockroach has to run into a shadow, cast by round plates standing on the table, in T seconds. Shadow casted by any of the plates has the shape of a circle. Shadow circles may intersect, nest or overlap arbitrarily.
The cockroach uses the following strategy: first he equiprobably picks a direction to run towards and then runs towards it with the constant speed v. If at some moment t≤T it reaches any shadow circle, it immediately stops in the shadow and thus will stay alive. Otherwise the cockroach is killed by the Dima's precise strike. Consider that the Dima's precise strike is instant.
Determine the probability of that the cockroach will stay alive.
At the moment 0 Dima saw a cockroach running on a table and decided to kill it. Dima needs exactly T seconds for aiming, and after that he will precisely strike the cockroach and finish it.
To survive the cockroach has to run into a shadow, cast by round plates standing on the table, in T seconds. Shadow casted by any of the plates has the shape of a circle. Shadow circles may intersect, nest or overlap arbitrarily.
The cockroach uses the following strategy: first he equiprobably picks a direction to run towards and then runs towards it with the constant speed v. If at some moment t≤T it reaches any shadow circle, it immediately stops in the shadow and thus will stay alive. Otherwise the cockroach is killed by the Dima's precise strike. Consider that the Dima's precise strike is instant.
Determine the probability of that the cockroach will stay alive.
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≤100000) is given− the number of shadow circles casted by plates.
In the next n lines shadow circle desc
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.
Examples
Input
0 0 1 1
3
1 1 1
-1 -1 1
-2 2 1
Output
0.50000000000
Input
0 0 1 0
1
1 0 1
Output
1.00000000000
Note
The picture for the first sample is given below. 
输入样例 复制
输出样例 复制