Description:
DZY loves Physics, and he enjoys calculating density.
Almost everything has density, even a graph. We define the density of a non-directed graph (nodes and edges of the graph have some values) as follows:
$$\begin{cases}
\dfrac{v}{e} & (e > 0) \\
0 & (e = 0)
\end{cases}$$
Once DZY got a graph G, now he wants to find a connected induced subgraph G' of the graph, such that the density of G' is as large as possible.
An induced subgraph G'(V', E') of a graph G(V, E) is a graph that satisfies:
- $$V' \subseteq V$$;
- edge $$(a,b)\in E^{T}$$ if and only if $$a \in V', b \in V'$$, and edge $$(a,b)\in E$$;
- the value of an edge in G' is the same as the value of the corresponding edge in G, so as the value of a node.
Help DZY to find the induced subgraph with maximum density. Note that the induced subgraph you choose must be connected.
Input Format:
The first line contains two space-separated integers n (1 ≤ n ≤ 500), $$m \left( 0 \leq m \leq \frac{n(n-1)}{2} \right)$$. Integer n represents the number of nodes of the graph G, m represents the number of edges.
The second line contains n space-separated integers xi (1 ≤ xi ≤ 106), where xi represents the value of the i-th node. Consider the graph nodes are numbered from 1 to n.
Each of the next m lines contains three space-separated integers ai, bi, ci (1 ≤ ai < bi ≤ n; 1 ≤ ci ≤ 103), denoting an edge between node ai and bi with value ci. The graph won't contain multiple edges.
Output Format:
Output a real number denoting the answer, with an absolute or relative error of at most 10 - 9.
Note:
In the first sample, you can only choose an empty subgraph, or the subgraph containing only node 1.
In the second sample, choosing the whole graph is optimal.