Score : $600$ points
Snuke's town has a subway system, consisting of $N$ stations and $M$ railway lines. The stations are numbered $1$ through $N$. Each line is operated by a company. Each company has an identification number.
The $i$-th ( $1 \leq i \leq M$ ) line connects station $p_i$ and $q_i$ bidirectionally. There is no intermediate station. This line is operated by company $c_i$.
You can change trains at a station where multiple lines are available.
The fare system used in this subway system is a bit strange. When a passenger only uses lines that are operated by the same company, the fare is $1$ yen (the currency of Japan). Whenever a passenger changes to a line that is operated by a different company from the current line, the passenger is charged an additional fare of $1$ yen. In a case where a passenger who changed from some company A's line to another company's line changes to company A's line again, the additional fare is incurred again.
Snuke is now at station $1$ and wants to travel to station $N$ by subway. Find the minimum required fare.
The input is given from Standard Input in the following format:
$N$ $M$ $p_1$ $q_1$ $c_1$ : $p_M$ $q_M$ $c_M$
Print the minimum required fare. If it is impossible to get to station $N$ by subway, print -1 instead.
3 3 1 2 1 2 3 1 3 1 2
1
Use company $1$'s lines: $1$ → $2$ → $3$. The fare is $1$ yen.
8 11 1 3 1 1 4 2 2 3 1 2 5 1 3 4 3 3 6 3 3 7 3 4 8 4 5 6 1 6 7 5 7 8 5
2
First, use company $1$'s lines: $1$ → $3$ → $2$ → $5$ → $6$. Then, use company $5$'s lines: $6$ → $7$ → $8$. The fare is $2$ yen.
2 0
-1