Problems
Count the triplets
Count the triplets
Given three array $a, b$ and $c$ of $n$ integers each. Find the number of triplets $(a_i, b_j, c_k)$ such that $a_i < b_j < c_k$.
\InputFile
First line contains the size of arrays $n\:(n \le 10^5)$. Second line contains elements of array $a$. Next line contains elements of array $b$. Last line contains elements of array $c$.
\OutputFile
Print the number of triplets $(a_i, b_j, c_k)$ such that $a_i < b_j < c_k$.
\Note
In the first test we have triples $(a_1, b_1, c_1), (a_1, b_2, c_1)$ and $(a_1, b_2, c_2)$.
Input example #1
2 1 5 4 2 6 3
Output example #1
3
Input example #2
3 1 1 1 2 2 2 3 3 3
Output example #2
27