Weighted Paths on NetworkX X15175

Given a directed graph with $n$ vertices and $m$ weighted arcs, we wish to know the cost of the minimum-cost directed path between two given vertices, if there is one.

Input

Input starts with $n$ and $m$. Then follow $m$ 3-tuples $u,v,w$, with $u \ne v$, indicating an arc from $u$ to $v$ with weight $w$. The following will be true: there are no repeated arcs, all weights are positive integers, $0 \leq u < n$ and $0 \leq v < n$. Finally, there follows a pair $x$, $y$ with $0 \leq x < n$ and $0 \leq y < n$.

Output

Write the total cost (sum of arc weights) of the path from $x$ to $y$ of least cost, if one exists; otherwise, write “no path”.

Observation

We are authorized to employ the NetworkX library.