Ant mansion collapse

An ant kingdom has $N+1$ ant nests, numbered from $0$ to $N$. There are $M$ bidirectional paths, each connecting two different nests. After a heavy rain, the kingdom is at risk of collapse, so the collapse risk of every path was measured. The collapse risk of path $i$ is $d_{i}$. By default, every path has a different risk. The exception is that paths directly connected to nest $0$ may have equal risks.

So, are the nests safe?

At the moment, $N$ ants numbered from $1$ to $N$ are gathered at nest $0$. Ant $i$ sets out on a trip to check whether nest $i$ is safe. The ants want to minimize the total risk of the paths they use. In other words, if the set of path numbers used by the $N$ ants is $S=\{s_{1}, s_{2}, \cdots, s_{M}\}$, they want to minimize the following value $W$.

$W=\sum_{i=1}^{M}{d_{s_{i}}}$

Each time an ant uses a path, it spends $1$ unit of stamina. Among the cases where $W$ is minimal, help the ants minimize the total stamina they spend.

The first line contains $N$ and $M$, separated by a space. $(1\leq N \leq 200\,000; 1 \leq M \leq 200\,000)$

Each of the next $M$ lines contains $u$, $v$, and $d$, separated by spaces. This means the path connecting nest $u$ and nest $v$ has risk $d$. $(0\leq u,v \leq N; u \neq v; 1\leq d \leq 10^{9})$

When $W$ is minimal, print the minimum total stamina the ants spend. If it is impossible to check all $N$ nests, print $-1$.