atac

The Siti republic of planet Krogos suffered a heavy air attack. A total of N bombs were dropped. The attackers, from the republic of Squari, use bombs that explode inside a rectangle and damage caused in this rectangle is the same all over it. The margins of the rectangle ARE NOT affected. Lurin, the president of the Siti republic, wants to start rescue and reconstruction operations immediately. To do this, he takes into account the extent of damage of a point on the surface of the republic as being the number of bombs that have affected that point. In order to send the rescue teams to the most affected areas the mayor asks you to determine the maximum extent of damage in the entire republic. He also wants to know the total size of the area that has this extent of damage.

Input Data

File atac.in contains on the first line the positive integer N.
The following N lines contain coordinates of rectangles affected by the bombs; line i contains x1i, y1i, x2i, y2i, positive integers between 0 and 100000 (including).

Output Data

File atac.out will contain a single line, with two positive integers - the first is the maximum extent of damage and the second represents the size of areas that were affected by the maximum number of bombs.

Restrictions

1 <= N <= 100000
0 <= x1i, y1i, x2i, y2i <= 100000
x1i < x2i
y1i < y2i

Example

atac.in atac.out
4 2 5
0 0 2 2
2 0 4 2
1 0 3 4
0 3 2 4

Time limit: 2 seconds/test

Radu Berinde
M.I.T.
radu.berinde#gmail.com