Problem Statement

There are $n$ sticks of each color: red, green, and blue. The lengths of the $i$-th stick of each color are $r_i, g_i, b_i$, respectively.

When making a triangle using the $i$-th red stick, the $j$-th green stick, and the $k$-th blue stick, compute the number of integer tuples $(i, j, k)$ such that a triangle with positive area is formed and $r_i = \max(r_i, g_j, b_k)$ is satisfied.

Constraints

Input

$n$
$r_1\ r_2\ \dots\ r_n$
$g_1\ g_2\ \dots\ g_n$
$b_1\ b_2\ \dots\ b_n$

Output

Output the answer on one line. End the output with a newline.

Sample

2
2 3
3 2
1 2

5

5
123 456 789 987 654
321 231 1 1 2
2 3 500 1000 1000

3