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: where v is the sum of the values of the nodes, e is the sum of the values of the edges.
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: ; edge if and only if , and edge ; 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 The first line contains two space-separated integers n(1 \le n \le 500), . 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 \le xi \le 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 \le ai \lt bi \le n;1 \le ci \le 103), denoting an edge between node ai and bi with value ci. The graph won't contain multiple edges.

Output Output a real number denoting the answer, with an absolute or relative error of at most 10-9.

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.