### 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.

### 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.

### Constraints

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

6

Consider the following arrangement: dog 1, cat 2, dog 2, cat 1, from left to right. Then,

• dog 1's frustration is 1×∣0−2∣=2;
• dog 2's frustration is 3×∣1−1∣=0;
• cat 1's frustration is 2×∣2−0∣=4; and
• cat 2's frustration is 4×∣1−1∣=0,

so the sum of the frustrations is 6. Rearranging the animals does not make the sum less than 6, so the answer is 6.