Problem Description

Given the positions of $n$ rectangular parallelepipeds in a three-dimensional space, determine how many pairs of these rectangles have overlapping parts. (A single point of intersection is also considered an overlap.)

Input Format

The first line of input contains an integer $n$, representing the number of rectangles.

The next $n$ lines each contain six integers. The first three integers represent the coordinates of the bottom-left vertex of the rectangle, and the last three integers represent the coordinates of the top-right vertex of the rectangle.

Output Format

Output a single integer on one line, representing the number of overlapping pairs of rectangles.

Sample Input and Output

Sample Input #1

3
1 1 1 1 3 3
1 3 3 1 6 6
1 4 4 1 5 5

Sample Output #1

2

Sample Input #2

3
15 10 10 15 20 20
10 15 10 20 15 20
10 10 15 20 20 15

Sample Output #2

3

Sample Input #3

5
4 4 5 4 3 2
5 3 2 4 3 1
5 4 3 1 1 3
1 4 3 1 5 4
5 5 4 5 4 2

Sample Output #3

4

Notes

Data Size and Constraints

For $100\%$ of the data, it is guaranteed that $1 \le n \le 10^5$, and the coordinates range between $1$ and $999$. Each rectangle is parallel to one of the coordinate planes.

Note

This problem is translated from COCI2006-2007 CONTEST #6 T6 PROSTOR.

见题面 Input 部分

见题面 Output 部分