Problem Statement

There are $N$ dogs numbered $1$ through $N$ and $M$ cats numbered $1$ through $M$. You will arrange the $(N+M)$ animals in a line from left to right. An arrangement causes each animal's frustration as follows:

• The frustration of dog $i$ is $A_i\times|x-y|$, where $x$ and $y$ are the numbers of cats to the left and right of that dog, respectively.
• The frustration of cat $i$ is $B_i\times|x-y|$, where $x$ and $y$ are the numbers of dogs to the left and right of that cat, respectively.

Find the minimum possible sum of the frustrations.

Constraints

• $1\leq N,M \leq 300$
• $1\leq A_i,B_i \leq 10^9$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N M
A_1 A_2 \ldots A_N
B_1 B_2 \ldots B_M

Output

Print the answer as an integer.