Problem: 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: 

<image> 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:

  * <image>; 
  * edge <image> if and only if <image>, and edge <image>; 
  * 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.

<image>

Input

The first line contains two space-separated integers n (1 ≤ n ≤ 500), <image>. 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.

Examples

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.

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Agostinho Junior (junior94)
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA {
	OutputWriter out;
	InputReader in;
	public void solve(int testNumber, InputReader in, OutputWriter out) {
		this.in = in; this.out = out;
		double ans = 0;
		int n = in.readInt();
		int m = in.readInt();
		int[] x = new int[n];
		for (int i = 0; i < n; i++) {
			x[i] = in.readInt();
		}
		while (m-- > 0) {
			int a = in.readInt() - 1;
			int b = in.readInt() - 1;
			int c = in.readInt();
			ans = Math.max(ans, 1.0 * (x[a] + x[b]) / c);
		}
		out.print(ans);
	}
}

class OutputWriter {
	private PrintWriter output;
	public OutputWriter() {
		this(System.out);
	}
	public OutputWriter(OutputStream out) {
		output = new PrintWriter(out);
	}
	public OutputWriter(Writer writer) {
		output = new PrintWriter(writer);
	}
	public void print(Object o) {
		output.print(o);
	}

	public void close() {
		output.close();
	}
}

class InputReader {
	private BufferedReader input;
	private StringTokenizer line = new StringTokenizer("");
	public InputReader() {
		this(System.in);
	}
	public InputReader(InputStream in) {
		input = new BufferedReader(new InputStreamReader(in));
	}
	public InputReader(String s) {
		try {
			input = new BufferedReader(new FileReader(s));
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}
	public void fill() {
		try {
			if(!line.hasMoreTokens()) line = new StringTokenizer(input.readLine());
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}

	public int readInt() {
		fill();
		return Integer.parseInt(line.nextToken());
	}
}