Migrated from Lutece 247 Tile

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Description

Squares and rectangles fascinated the famous Dutch painter Piet Mondriaan. One night, after producing the drawings in his toilet series (where he had to use his toilet paper to draw on, for all of his paper was filled with squares and rectangles), he dreamt of filling a large rectangle whose some cells can't be filled with small rectangles of width $2$ and height $1$ in varying ways.

Expert as he was in this material, he saw at a glance that he'll need a computer to calculate the number of ways to fill the given large rectangle whose dimensions were integer values, as well. Help him, so that his dream won't turn into a nightmare!

Input

On the first line of the input is a single positive integer $C$, telling the number of test scenarios to follow. The first line of each test case contains three integer numbers: the height $h$ and the width $w$ of the large rectangle and the number of prohibit positions $n$. Then followed with $n$ lines. Each line contains two integers row and col, meaning the cell in (row, col) can't be filled. Note $1 \leq row \leq h$ and $1 \leq col \leq w , 1 \leq h,w \leq11$.

Output

For each test case, output the number of different ways the given rectangle can be filled with small rectangles of size 2 times 1. Assume the given large rectangle is oriented, i.e. count symmetrical tilings multiple times.

Samples

3
2 2 0
2 3 2
1 1
2 3
11 10 0

2
1
3852472573499

Note

Case $1$:a $2 \times 2$ rectangle with no obstacle ,you put $2$ $2 \times 1$ rectangles vertically or horizontally to fill it,so there're $2$ ways in total.

Case 2:a rectangle as below (x stands for obstacle and o stands for available grid):

xoo
oox

only one way to fill it(grid with the same number belongs to one $2 \times 1$ rectangle)

x11
22x

Resources

modified from Ulm Local 2000