A small group of commandos has infiltrated deep into enemy territory. They have just accomplished
their mission and now have to return to their rendezvous point. Of course they
don’t want to get caught even if the mission is already over. Therefore they decide to take
the route that will keep them as far away from any enemy base as possible.
Being well prepared for the mission, they have a detailed map of the area which marks
all (known) enemy bases, their current position and the rendezvous point. For simplicity,
we view the the map as a rectangular grid with integer coordinates (x, y) where 0 <= x <
X, 0 <= y < Y . Furthermore, we approximate movements as horizontal and vertical steps
on this grid, so we use Manhattan distance: dist((x1, y1), (x2, y2)) = |x2 −x1|+|y2 −y1|. The
commandos can only travel in vertical and horizontal directions at each step.
Can you help them find the best route? Of course, in case that there are multiple routes
that keep the same minimum distance to enemy bases, the commandos want to take a shortest
route that does so. Furthermore, they don’t want to take a route off their map as it could
take them in unknown, dangerous areas, but you don’t have to worry about unknown enemy
bases off the map.
Input
On the first line one positive number: the number of testcases, at most 100. After that per
testcase:
• One line with three positive numbers N,X, Y . 1 <= N <= 10 000 is the number of enemy
bases and 1 <= X, Y <= 1 000 the size of the map: coordinates x, y are on the map if
0 <= x < X, 0 <= y < Y .
• One line containing two pairs of coordinates xi, yi and xr, yr: the initial position of the
commandos and the rendezvous point.
• N lines each containing one pair of coordinates x, y of an enemy base.
All pairs of coordinates are on the map and different from each other.
Output
Per testcase:
• One line with two numbers separated by one space: the minimum separation from an
enemy base and the length of the route.
Sample Input
2
1 2 2
0 0 1 1
0 1
2 5 6
0 0 4 0
2 1
2 3
Sample Output
1 2
2 14
Hint
Source
The 2007 ACM Northwestern European Programming Contest