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.
输入描述:
The first line contains two space-separated integers n (1 ≤ n ≤ 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 ≤ 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.
输出描述:
Output a real number denoting the answer, with an absolute or relative error of at most 10 - 9.
示例1
输入
1 0<br />1<br />2 1<br />1 2<br />1 2 1<br />5 6<br />13 56 73 98 17<br />1 2 56<br />1 3 29<br />1 4 42<br />2 3 95<br />2 4 88<br />3 4 63<br />
输出
0.000000000000000<br />3.000000000000000<br />2.965517241379311<br />
备注:
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.
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