You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
As Kevin is in BigMan's house, suddenly a trap sends him onto a grid with $$$n$$$ rows and $$$m$$$ columns.

BigMan's trap is configured by two arrays: an array $$$a_1,a_2,\ldots,a_n$$$ and an array $$$b_1,b_2,\ldots,b_m$$$.

In the $$$i$$$-th row there is a heater which heats the row by $$$a_i$$$ degrees, and in the $$$j$$$-th column there is a heater which heats the column by $$$b_j$$$ degrees, so that the temperature of cell $$$(i,j)$$$ is $$$a_i+b_j$$$.

Fortunately, Kevin has a suit with one parameter $$$x$$$ and two modes:

- heat resistance. In this mode suit can stand all temperatures greater or equal to $$$x$$$, but freezes as soon as reaches a cell with temperature less than $$$x$$$.
- cold resistance. In this mode suit can stand all temperatures less than $$$x$$$, but will burn as soon as reaches a cell with temperature at least $$$x$$$.

Once Kevin lands on a cell the suit automatically turns to cold resistance mode if the cell has temperature less than $$$x$$$, or to heat resistance mode otherwise, and cannot change after that.

We say that two cells are adjacent if they share an edge.

Let a path be a sequence $$$c_1,c_2,\ldots,c_k$$$ of cells such that $$$c_i$$$ and $$$c_{i+1}$$$ are adjacent for $$$1 \leq i \leq k-1$$$.

We say that two cells are connected if there is a path between the two cells consisting only of cells that Kevin can step on.

A connected component is a maximal set of pairwise connected cells.

We say that a connected component is good if Kevin can escape the grid starting from it  — when it contains at least one border cell of the grid, and that it's bad otherwise.

To evaluate the situation, Kevin gives a score of $$$1$$$ to each good component and a score of $$$2$$$ for each bad component.

The final score will be the difference between the total score of components with temperatures bigger than or equal to $$$x$$$ and the score of components with temperatures smaller than $$$x$$$.

There are $$$q$$$ possible values of $$$x$$$ that Kevin can use, and for each of them Kevin wants to know the final score.

Help Kevin defeat BigMan!

## Input Format
The first line contains three integers $$$n$$$,$$$m$$$,$$$q$$$ ($$$1 \leq n,m,q \leq 10^5$$$)  – the number of rows, columns, and the number of possible values for $$$x$$$ respectively.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \leq a_i \leq 10^5$$$).

The third line contains $$$m$$$ integers $$$b_1, b_2, \dots, b_m$$$ ($$$1 \leq b_i \leq 10^5$$$).

Each of the next $$$q$$$ lines contains one integer $$$x$$$ ($$$1 \leq x \leq 2 \cdot 10^5$$$).

## Output Format
Output $$$q$$$ lines, in the $$$i$$$-th line output the answer for the $$$i$$$-th possible value of $$$x$$$ from the input.

## Examples
```input
5 5 1
1 3 2 3 1
1 3 2 3 1
5
```
```output
-1
```
-----
```input
3 3 2
1 2 2
2 1 2
3
4
```
```output
0
1
```

## Note
In the first example, the score for components with temperature smaller than $$$5$$$ is $$$1+2$$$, and the score for components with temperature at least $$$5$$$ is $$$2$$$. Thus, the final score is $$$2-3=-1$$$.

Now solve the problem and return the code.