Migrated from Lutece 403 Finding Nemo

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Description

Nemo is a naughty boy. One day he went into the deep sea all by himself. Unfortunately, he became lost and couldn't find his way home. Therefore, he sent a signal to his father, Marlin, to ask for help.

After checking the map, Marlin found that the sea is like a labyrinth with walls and doors. All the walls are parallel to the $X$-axis or to the $Y$-axis. The thickness of the walls are assumed to be zero.

All the doors are opened on the walls and have a length of $1$. Marlin cannot go through a wall unless there is a door on the wall. Because going through a door is dangerous (there may be some virulent medusas near the doors), Marlin wants to go through as few doors as he could to find Nemo.

Figure-$1$ shows an example of the labyrinth and the path Marlin went through to find Nemo.

We assume Marlin's initial position is at $(0, 0)$. Given the position of Nemo and the configuration of walls and doors, please write a program to calculate the minimum number of doors Marlin has to go through in order to reach Nemo.

Input

The first line of the input is an integer $T$ ($T \leq 100$), which stands for the number of test cases you need to solve.

Each test case is started by two non-negative integers $M$ and $N$. $M$ represents the number of walls in the labyrinth and $N$ represents the number of doors.

Then follow $M$ lines, each containing four integers that describe a wall in the following format:x y d t

$(x, y)$ indicates the lower-left point of the wall, $d$ is the direction of the wall -- $0$ means it's parallel to the $X$-axis and $1$ means that it's parallel to the $Y$-axis, and $t$ gives the length of the wall.

The coordinates of two ends of any wall will be in the range of $[1,199]$.

Then there are $N$ lines that give the description of the doors:x y d $x, y, d$ have the same meaning as the walls. As the doors have fixed length of $1$, $t$ is omitted.

The last line of each case contains two positive float numbers:f1 f2 $(f_1, f_2)$ gives the position of Nemo. And it will not lie within any wall or door.

Output

For every test case, you should output Case #k: first, where $k$ indicates the case number and starts at $1$. please output the minimum number of doors Marlin has to go through in order to rescue his son. If he can't reach Nemo, output $-1$.

Samples

2
8 9
1 1 1 3
2 1 1 3
3 1 1 3
4 1 1 3
1 1 0 3
1 2 0 3
1 3 0 3
1 4 0 3
2 1 1
2 2 1
2 3 1
3 1 1
3 2 1
3 3 1
1 2 0
3 3 0
4 3 1
1.5 1.5
4 0
1 1 0 1
1 1 1 1
2 1 1 1
1 2 0 1
1.5 1.7

Case #1: 5
Case #2: -1

Resources

Beijing 2004