Building Snowmen

You want to build an army of snowmen. To do so, you have gathered a bunch of snowballs of varying sizes. Each snowman is built by stacking three snowballs on top of one another: first choose a snowball for the base, then a smaller one for the middle, and finally an even smaller one for the top.

Each snowball has a diameter $d$. For a given snowman, let the diameter of the base snowball be $d_b$, the diameter of the middle snowball be $d_m$, and the diameter of the top snowball be $d_t$. Then both of the following inequalities must hold:

• $2 d_b \geq 3 d_m$
• $2 d_m \geq 3 d_t$

Compute the maximum number of snowmen that can be built from the available snowballs while satisfying these conditions.

The first line contains the number of data sets $K$. Then $K$ data sets follow, each in the form below.

The first line of each data set contains the number of snowballs $N$ ($3 \leq N \leq 1000$). The next line contains $N$ integers, each between $1$ and $1000$ inclusive. The $i$-th integer is the diameter of the $i$-th snowball.

For each data set, first output Data Set x: on its own line, where $x$ is the data set's number. On the next line, output the maximum number of proper snowmen that can be completed. Separate consecutive data sets with a single blank line.