CF266D.BerDonalds

BerDonalds, a well-known fast food restaurant, is going to open a cafe in Bertown. The important thing is to choose the new restaurant's location so that it would be easy to get there. The Bertown road system is represented by n junctions, connected by m bidirectional roads. For each road we know its length. We also know that we can get from any junction to any other one, moving along the roads.

Your task is to find such location of the restaurant, that the shortest distance along the roads from the cafe to the farthest junction would be minimum. Note that the restaurant can be located not only on the junction, but at any point of any road.

知名快餐连锁店 BerDonalds 计划在 Bertown 市开设一家咖啡馆。关键在于选择一个合适的咖啡馆位置，使其便于到达。Bertown 的道路系统由 $n$ 个路口组成，这些路口通过 $m$ 条双向道路连接。每条道路的长度已知。此外，我们还知道：沿着道路，可以从任意一个路口到达其他任意一个路口。

你的任务是确定咖啡馆的位置，使得从咖啡馆到最远路口的最短道路距离最小。注意：咖啡馆不仅可以建在路口处，也可以建在任意一条道路的任意一点上。

The first line contains two integers n and m () — the number of junctions and the number of roads, correspondingly. Then m lines follow, describing all Bertown roads. Each road is described by three integers a__i, b__i, w__i (1 ≤ a__i, b__i ≤ n, a__i ≠ b__i; 1 ≤ w__i ≤ 105), where a__i and b__i are the numbers of the junctions, connected by the i-th road, and w__i is the length of the i-th road.

It is guaranteed that each road connects two distinct junctions, there is at most one road between any two junctions, and you can get from any junction to any other one.

第一行包含两个整数 $n$ 和 $m$（），分别表示路口的数量和道路的数量。接下来有 $m$ 行，描述 Bertown 的所有道路。每条道路由三个整数 $a_i,\,b_i,\,w_i$（$1 \le a_i,\,b_i \le n$，$a_i \ne b_i$；$1 \le w_i \le 10^5$）描述，其中 $a_i$ 和 $b_i$ 是第 $i$ 条道路所连接的两个路口的编号，$w_i$ 是第 $i$ 条道路的长度。

保证每条道路均连接两个不同的路口，任意两个路口之间至多存在一条道路，且从任一路口均可到达其他任意路口。

Print a single real number — the shortest distance from the optimal restaurant location to the farthest junction. The answer will be considered correct, if its absolute or relative error doesn't exceed 10 - 9.

输出一个实数——最优餐厅位置到最远路口的最短距离。若答案的绝对误差或相对误差不超过 $10^{-9}$，则视为正确。