Potential Graph 1

Given an undirected simple connected graph $G = (V,E)$ with weighted edges. For a function $f: V \to \mathbb{R}$ defined on the vertices of $G$, define $g_f: V \to \mathbb{R}$ as follows. $g_f(u) = \sum_{v: (u,v) \in E} (f(u) - f(v)) \cdot w(u,v)$ Here $\sum_{v: (u,v) \in E}$ is the sum over all vertices $v$ adjacent to $u$, and $w(u,v) = w(v,u) > 0$ is the weight of the edge $(u,v) \in E$ connecting $u$ and $v$. The vertices of $G$ are the integers from 1 to $N$. The following three conditions uniquely determine $f$ and $g_f$: (1) $f(1) = 1$. (2) $f(N) = 0$. (3) $g_f(u) = 0$ for every integer $u$ with $1 < u < N$. Given $G$, write a program that prints $g_f(1)$.

The first line contains the number of vertices $N$ and the number of edges $M$ of $G$, separated by a space. $(2 \le N \le 100$, $N-1 \le M \le \frac{N(N-1)}{2})$ From the second line, the next $M$ lines each contain three positive integers $u$, $v$, and $w$, separated by spaces. This means there is an edge connecting vertices $u$ and $v$ with weight $w$. $(1 \le u, v \le N$, $u \ne v$, $1 \le w \le 100)$ Each pair of vertices is connected by at most one edge.

Print the value of $g_f(1)$. An absolute or relative error of up to $10^{-6}$ is allowed.