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:

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?≤?n?≤?500), . Integer n represents the number of nodes of the graph G, m represents the number of edges.<??http://www.2cto.com/kf/ware/vc/" target="_blank" class="keylink">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"t contain multiple edges.

  Output

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

  Sample test(s) 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
  

  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.

  
  

  证明：必然存在一条边数≤1的最优解

  假设存在最优解(G)ans最小边数>1，则点数>2

  ans=∑vi/∑c

  由假设知对G的子图,(u+v)/c

  ∴∑u+∑v

  ∴(∑u+∑v)<∑vi 矛盾

  结论成立

  
  

  所以只要判断所有的只取1条边，和不取的情况 O(m)

  
  

  
  

  
  
  

  
  

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                 using namespace std; #define For(i,n) for(int i=1;i<=n;i++) #define Fork(i,k,n) for(int i=k;i<=n;i++) #define Rep(i,n) for(int i=0;i
                
                 =0;i--) #define Forp(x) for(int p=pre[x];p;p=next[p]) #define Lson (x<<1) #define Rson ((x<<1)+1) #define MEM(a) memset(a,0,sizeof(a)); #define MEMI(a) memset(a,127,sizeof(a)); #define MEMi(a) memset(a,128,sizeof(a)); #define INF (2139062143) #define F (100000007) #define MAXN (500+10) #define MAXM (MAXN*MAXN) #define MAXAi (1e6) #define MAXCi (1e3) long long mul(long long a,long long b){return (a*b)%F;} long long add(long long a,long long b){return (a+b)%F;} long long sub(long long a,long long b){return (a-b+(a-b)/F*F+F)%F;} typedef long long ll; typedef long double ld; int n,m,a[MAXN]; ld ans=0.0; int main() { // freopen("Physics.in","r",stdin); scanf("%d%d",&n,&m); For(i,n) scanf("%d",&a[i]); For(i,m) { int u,v; double c; scanf("%d%d%lf",&u,&v,&c); ans=max(ans,(ld)(a[u]+a[v])/c); } cout<