Salmon received an array $A$ of size $N$ and an array $B$ of size $M$ for Christmas. He would like to move all the elements in $B$ to $A$ using a special method described below.

While $B$ is not empty, Salmon does the following operations in order:

• Remove and store the leftmost element off of B (let's call this element $X$).
• Place $X$ at the start of $A$.
• Keep swapping $X$ and the element to the right of it repeatedly until $X$ is at the rightmost position of $A$ or $X$ is greater or equal to the element to the right of it.

Before performing the operations, Salmon can rearrange both A and B in any order once. He would like to do as little work as possible -- determine the minimum possible amount of swaps.

------ Input: ------
The first line of input will consist of a two space-separated integers, $N$ and $M$ ($1 ≤ N, M ≤ 2*10^{5}$).

The next line will consist of $N$ space-separated integers, with the $i$-th input representing $A[i]$ ($-10^{9} ≤ A[i] ≤ 10^{9}$).

The next line will consist of $M$ space-separated integers, with the $i$-th input representing $B[i]$ ($-10^{9} ≤ B[i] ≤ 10^{9}$).

------ Output: ------
Output a single integer, the minimum number of swaps required.

------ Subtasks: ------
* Subtask 1 [15 points]: $A[i] = 1, B[i] = 1$ for all $i$.
* Subtask 2 [30 points]: $N, M ≤ 10^{3}$.
* Subtask 3 [55 points]: No additional constraints.

------ Note: ------
The answer may be greater than the limit for a 32-bit integer. Use long long instead of int for C++ and long for Java. Please check your language documentation for other languages on how to use 64-bit integers. Note that Python solutions won't encounter a problem as it uses BigIntegers by default.

----- Sample Input 1 ------
5 3
10 5 2 5 4
3 1 2
----- Sample Output 1 ------
5
----- explanation 1 ------
Salmon can reorder $A$ to be $[2, 10, 5, 4, 5]$ and $B$ to be $[1, 2, 3]$.

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