Problem Description

In a three-dimensional space, there are $N$ cubes. The $i$-th cube occupies the region from $(x_{i_1}, y_{i_1}, z_{i_1})$ to $(x_{i_2}, y_{i_2}, z_{i_2})$. These $N$ cubes may intersect or overlap. Together, they form a large geometric shape. Now, find the outer surface area of this shape.

Input Format

The first line contains an integer $N$, representing the number of cubes.

Lines $2$ to $N+1$ each contain $6$ integers separated by spaces, representing $x_1$, $y_1$, $z_1$, $x_2$, $y_2$, $z_2$.

Output Format

Output one line containing an integer, representing the outer surface area.

1
0 0 0 1 1 1

6

2 
0 1 0 3 2 1
1 0 0 2 3 1

22

Hint

All testdata satisfy $\in~[0,200]$.

$x_1~\leq~x_2$.

$y_1~\leq~y_2$.

$z_1~\leq~z_2$.

Translated by ChatGPT 5