Safest Pens

Bessie and her cow compatriots feel safest when they are surrounded by a fence -- and even safer when surrounded by two fences. On the farm's pastures there are N (1 <= N <= 100,000) rectangular fences. The fences don't overlap or touch, however any given fenced area might wholly contain one or more other areas.

Bessie and the other cows want to graze within a pen that is surrounded by as many other pens as possible. Furthermore she wants to
know how many of those 'safest places' there exist in the pastures.
Help Bessie learn these numbers.

PROBLEM NAME: safepens

INPUT FORMAT:

* Line 1: A single line with the single integer, N

* Lines 2..N+1: Each line contains four space-separated integers
        (respectively X1, Y1, X2 and Y2) that are the coordinates of
        the lower left and upper right corner of the fences.  All
        coordinates are in the range 1..1,000,000,000 and both X1<X2
        and Y1<Y2.

SAMPLE INPUT:

4
1 1 16 16
6 6 11 13
7 7 9 12
3 3 10 5

OUTPUT FORMAT:

* Line 1: Two space-separated integers: the maximal number of fences
        that can surround Bessie and how many such places have this
        property.

SAMPLE OUTPUT:

3 1

OUTPUT DETAILS:

The 3rd fence is surrounded by fence 1 and 2, so Bessie can be
within 3 fences. There is only 1 such place.