dzy loves physics

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.;

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 ≤ 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.

Output

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

Sample Input

Input

1 0

1

Output

0.000000000000000

Input

2 1

1 2

1 2 1

Output

3.000000000000000

Input

5 6
13 56 73 98 17

1 2 56

1 3 29

1 4 42

2 3 95

2 4 88

3 4 63

Output
2.965517241379311

#include<stdio.h>
struct graph
{
int node1;
int node2;
int edgval;
};
int main( )
{
int n,m,i,index1,index2;
double max;
int a[505];
struct graph num[1500];
while(scanf("%d%d",&n,&m)!=EOF)
{
for(i=0;i<n;i++)
scanf("%d",&a[i]);
for(i=0;i<m;i++)
scanf("%d%d%d",&num[i].node1,&num[i].node2,&num[i].edgval);
if(num[0].edgval!=0)
{
index1=num[0].node1-1;
index2=num[0].node2-1;
max=(double)(a[index1]+a[index2])*1.0/num[0].edgval*1.0;
}
else max=0;
for(i=1;i<m;i++)
{
index1=num[i].node1-1;
index2=num[i].node2-1;
if(num[i].edgval!=0)
if((double)(a[index1]+a[index2])*1.0/num[i].edgval*1.0>=max)max=(double)(a[index1]+a[index2])*1.0/num[i].edgval*1.0;
else max=0;
}
printf("%.15lf\n",max);
}
return 0;
}