The Great Truce#1406
The heat dried all the moisture from the soil until the Vengunga River became a single stream. The wild elephant Hathi, who had lived for a hundred years or more, raised his trunk and declared the start of the Water Truce, just as his father had done fifty years earlier.
The smallest animals, such as the musk shrews, are best able to cope with water shortages. Taking advantage of the Vengunga River being shallower, the tribe of shrews decided to relocate to the opposite bank and, at the same time, redistribute their supplies: that is, from each burrow on one bank, a portion of supplies must be carried to every burrow on the other bank. During the Water Truce, according to Hathi's decree, it is only allowed to cross the Vengunga River perpendicularly to the current.
Calculate the sum of all the shortest distances for each pair of burrows on different banks of the Vengunga River.
Assume the river is modeled as a strip in the plane, with one bank specified by two points and the other bank by a single point.
The first line contains the integer (1 \le n \le 5000), the number of shrew burrows. The next lines each contain a pair of numbers denoting the coordinates of the shrew burrows. All coordinates are within 10^9 in absolute value. Next, the coordinates of three points defining the river banks are given (the first two points define one of the banks). Each point lies on one side of the river, i.e., there are no points located between the banks or on their boundary.
Print the sum of all the shortest distances for each pair of burrows on different banks of the Vengunga River. The answer should be output with an accuracy of 10^{-4}.
Example 1