Computational geometry is the key to modern programming contests.
You are given circles, the -th of which will appear with probability . Your task is to compute the expected area of the union of the appeared circles. Note that the appearance of the circles are mutually independent random events.

输入描述:

The first line contains an integer .
The following  lines describe the given  circles. The -th line contains four integers ,  and , describing the i-th circle whose center is , the radius is  and the probability of appearance is .

输出描述:

Output one number - the answer. Your answer will be considered correct if its relative or absolute error doesn’t exceed .

5
1 1 1 600
1 1 1 100
1 2 1 700
0 0 3 500
10 10 1 1000

19.1944414132