## Rectangle Counting

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Points: 17 (partial)
Time limit: 1.2s
Python 1.6s
Memory limit: 256M

Author:
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In the sport of rectangle counting, participants are given a set of rectangles and race to count the number of intersecting pairs. In order to check the answer, judges are called in to verify that the number of pairs counted by each contestant is correct.

The other day, Angie was invited to judge one of the competitions and now has to produce the correct answer for today's set of rectangles. Her schedule is very busy so she doesn't have the time to do all the calculations, can you help her?

#### Constraints

Note that the corners of the rectangle are and .

Note the difference in constraints above.

#### Input Specifications

The first line of input contains the integer .

The next lines of input each contain , representing the corners of the rectangle.

#### Output Specifications

Output the number of pairs of rectangles that intersect with one another. Note that two pairs and are considered the same pair and that two rectangles that are merely touching do not count as intersecting.

#### Sample Input

4
1 7 10 12
5 3 15 9
14 5 16 10
16 1 17 20

#### Sample Output

2

#### Sample Explanation

The intersecting pairs of rectangles are:

Note that the pairs and aren't counted.

Furthermore, even though the pair is touching they aren't counted because they don't fully intersect.