I'm trying to solve the following problem from Hanoi Olympiad in Informatics.

Problem: Given arrays $$$A$$$ $$$a_1,a_2,\ldots, a_m$$$ and $$$B$$$ $$$b_1,b_2,\ldots, b_n$$$. From $$$A$$$ we take $$$a_j, a_k$$$ and from $$$B$$$ we take $$$b_i$$$ such that the tuple formed by these numbers satisfies $$$a_j < b_i < a_k$$$ or $$$a_k < b_i < a_j$$$. Such triple is called special. These numbers will be remove from the original arrays, and we repeat the process with the remaining numbers of the arrays. Find the maximum number of special triples.

Input: First line contains $$$m, n$$$ ($$$2\le m\le 10^5, 2\le n\le 10^5$$$). The second line contains $$$a_1,a_2,\ldots, a_m$$$ ($$$1\le a_i\le 10^9$$$) and the third line contains $$$b_1,b_2,\ldots, b_n$$$ ($$$1\le b_i\le 10^9$$$).

Output: Maximum number of special triples.

**Example: **

Input:

5 3

5 1 3 2 2

2 4 3

Output:

2

Explanation: We can choose $$$a_1=5$$$, $$$a_4=2$$$, $$$b_2=4$$$ and $$$a_2=1$$$, $$$a_3=3$$$, $$$b_1=2$$$.