B"Shichikuji is the new resident deity of the South Black Snail Temple. Her first job is as follows: There are n new cities located in Prefecture X. Cities are numbered from 1 to n . City i is located x_i km North of the shrine and y_i km East of the shrine. It is possible that (x_i, y_i) = (x_j, y_j) even when i ne j . Shichikuji must provide electricity to each city either by building a power station in that city, or by making a connection between that city and another one that already has electricity. So the City has electricity if it has a power station in it or it is connected to a City which has electricity by a direct connection or via a chain of connections. Shichikuji wants to do this job spending as little money as possible, since according to her, there isn't really anything else in the world other than money. However, she died when she was only in fifth grade so she is not smart enough for this. And thus, the new resident deity asks for your help. And so, you have to provide Shichikuji with the following information: minimum amount of yen needed to provide electricity to all cities, the cities in which power stations will be built, and the connections to be made. If there are multiple ways to choose the cities and the connections to obtain the construction of minimum price, then print any of them. First line of input contains a single integer n ( 1 <= q n <= q 2000 ) -- the number of cities. Then, n lines follow. The i -th line contains two space-separated integers x_i ( 1 <= q x_i <= q 10^6 ) and y_i ( 1 <= q y_i <= q 10^6 ) -- the coordinates of the i -th city. The next line contains n space-separated integers c_1, c_2, ... , c_n ( 1 <= q c_i <= q 10^9 ) -- the cost of building a power station in the i -th city. The last line contains n space-separated integers k_1, k_2, ... , k_n ( 1 <= q k_i <= q 10^9 ). In th"...