cheesecake works part-time at the Centre for Disease Control and Prevention (CDC), where he researches the spread of diseases. An unknown pathogen has just broken out and cheesecake is determined to save the world!
The CDC’s model of the world consists of countries numbered through , represented by points on a 2-D coordinate plane. Country is located at integral coordinates .
Through extensive research, cheesecake has determined a vital piece of information: the time in hours it takes for the pathogen to spread from one country to another is equal to the square of the distance between the two countries. For example, if country is located at and country is located at , it will take hours for country to be infected after the initial infection of country . The source of the breakout, country , is infected at the -th hour.
In order to take preventative measures, cheesecake has been tasked with projecting the rate of infection. Specifically, he has to answer queries of the following form:
How many countries will be infected after hours?
Unfortunately, cheesecake isn't taking data management this semester, so he's at a total loss. Help him save the world!
Subtask 1 [20%]
Subtask 2 [30%]
Subtask 3 [50%]
Note: For PyPy 2 and PyPy 3 and Haskell, the time limit is s and the memory limit is M.
The first line of input will contain , the number of countries.
The next lines will contain and , the coordinates of the -th country, it is guaranteed that no two countries will have the same coordinates.
The next line will contain , the source of the breakout.
The next line will contain , the number of queries.
The next lines will each contain a query.
For each query, output the answer on a new line.
4 2 2 0 3 5 1 4 0 1 4 8 10 4 7
3 4 1 2
Explanation for Sample Output
After hours, the pathogen has not yet spread from its source, therefore answer is . After hours, country is infected. After hours, country is also infected. At hours, the pathogen has spread from country to country .