A Midsummer Night's Dream

In the comedy A Midsummer Night's Dream, Helena loves Demetrius, Demetrius loves Hermia, and Hermia loves Lysander, who loves her back. Hermia's father wants to force her to marry Demetrius, so she and Lysander run away. Demetrius chases them, and Helena chases Demetrius. Once the fairies hear about this mess, they decide to spend part of their own love potion on the humans instead. The potion, applied to the eyelids of a sleeping person, makes that person fall in love with the first person they see after waking up. Puck, the sprite who applies the potion, cannot tell the humans apart yet and puts it on the wrong people.

Count how many real couples come out of Puck's mistakes. A couple is two people who love each other.

For every person you are given the places where the person was seen and when, plus the time the potion was applied. You are also given the distance $d$ that people can see. From the moment the potion is applied to person $v$, $v$ falls in love with the first person whose distance to $v$ is at most $d$. Someone already inside the range of $v$ at the exact moment Puck applies the potion counts as a candidate. If several people are inside the range of $v$ at that same first moment, $v$ falls in love with the closest one. The input never makes two candidates equally close. Distance is Euclidean, and a distance of exactly $d$ is inside the range. Nobody falls in love with themselves, and if nobody ever comes inside the range, $v$ loves nobody.

The first line contains $K$ ($K \ge 1$), the number of data sets. $K$ data sets follow, each in this form.

The first line of a data set contains two integers $n$ and $d$. $1 \le n \le 100$ is the number of people and $0 \le d \le 100$ is the distance people can see.

Then come the descriptions of the $n$ people, numbered $1$ through $n$. For person $i$, one line contains two integers $p_i$ and $m_i$. $-1 \le p_i \le 10^4$ is the time when the potion was applied to person $i$, and $p_i = -1$ means the potion was never applied to $i$. $0 \le m_i \le 100$ is the number of locations at which $i$ was seen. The next line contains the three integers $x_{i,j}$, $y_{i,j}$, $t_{i,j}$ repeated $m_i$ times. $-1000 \le x_{i,j}, y_{i,j} \le 1000$ are the coordinates of the $j$th sighting of $i$, and $t_{i,j} \le 10^4$ is the time of that sighting. For each person the triples are sorted by increasing $t_{i,j}$.

Person $i$ stays at $(x_{i,j}, y_{i,j})$ from time $t_{i,j}$ until the next sighting at time $t_{i,j+1}$, or until time is over if there is no next sighting. Before the first sighting, person $i$ is somewhere far away: nobody sees $i$ and $i$ sees nobody. A person with $m_i = 0$ stays far away the whole time.

No two potion applications happen at the same time, and no potion application happens at the same time as a sighting. Two different people can be sighted at the same time.

For each data set, output Data Set x: on a line by itself, where $x$ is the number of the data set, counting from $1$. Then, on a line by itself, output the number of couples, that is the number of pairs of people who love each other. Follow each data set with a blank line.