Anisie, after suffering a series of successive disappointments at her former workplace, decides to escape the urbanism of Bucharest for that of Mizil. Mizil is kind of like New York in Romania. There, she finds a job as a tour guide.

Mizil can be described as a graph with $$$N$$$ tourist points and $$$M$$$ bidirectional streets connecting these points. Each street can be described by the points $$$x_i, y_i$$$ that it connects and a congestion value $$$c_i$$$, which indicates how unpleasant it is to traverse completely due to various factors, one of them being the presence of traffic jams. There can be no more than one street connecting any two touristic points.

Anisie organizes tours through Mizil. A tour is defined as a sequence of tourist points $$$t_1, t_2, \dots, t_k$$$, where any two successive tourist points are connected by a street. When planning these tours, two parameters must be taken into account:

• The level of discomfort, which is the highest congestion value of any street from $$$t_i$$$ to $$$t_{i+1}$$$ traversed during the tour.
• The level of luminosity. For a tourist point, we define its neon coefficient as the number of streets originating from it. The level of luminosity will be the smallest neon coefficient of any tourist point in the tour.

Ideally, Anisie would minimize the discomfort and maximize the luminosity. However, since each tourist has different needs, she will have to determine, given Mizil's map, for $$$Q$$$ triplets $$$u_i, v_i, l_i$$$, what is the minimum discomfort possible for a tour that starts at $$$u_i$$$, ends at $$$v_i$$$, and has a luminosity level of at least $$$l_i$$$. If no such tour exists, the result will be $$$-1$$$.