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.*;
import java.util.*;
import java.lang.*;
import java.math.*;

import static java.lang.Math.*;

public class Solution implements Runnable {
	
	void solve() throws Exception {
		int n = sc.nextInt();
		int a[][] = new int[n][n];
		int e[] = new int[n];
		int m = sc.nextInt();
		for (int i = 0; i < n; i++) {
			e[i] = sc.nextInt();
		}
		double ans = 0.0;
		for (int i = 0; i < m; i++) {
			int v = sc.nextInt(), u = sc.nextInt(), w = sc.nextInt();
			--v;
			--u;
			a[v][u] = a[u][v] = w;
		}
		for (int i = 0; i < n; i++) {
			for (int j = i + 1; j < n; j++) {
				if (a[i][j] > 0)
					ans = max(ans, (double)(e[i] + e[j]) / a[i][j]);
			}
		}
		out.format("%.12f%n", ans);
	}
	
	BufferedReader in;
	PrintWriter out;
	FastScanner sc;
	
	static Throwable throwable;
	
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			//in = new BufferedReader(new FileReader(".in"));
			//out = new PrintWriter(".out");
			sc = new FastScanner(in);
			solve();
		} catch (Exception e) {
			throwable = e;
		} finally {
			out.close();
		}
	}

	public static void main(String[] args) throws Throwable {
		Thread thread = new Thread(null, new Solution(), "", (1 << 26));
		thread.start();
		thread.join();
		thread.run();
		if (Solution.throwable != null)
			throw Solution.throwable;
	}

}

class FastScanner {
	BufferedReader reader;
	StringTokenizer strTok;
	
	public FastScanner(BufferedReader reader) {
		this.reader = reader;
	}
	
	public String nextToken() throws Exception {
		while (strTok == null || !strTok.hasMoreTokens())
			strTok = new StringTokenizer(reader.readLine());
		return strTok.nextToken();
	}
	
	public int nextInt() throws Exception {
		return Integer.parseInt(nextToken());
	}
	
	public long nextLong() throws Exception {
		return Long.parseLong(nextToken());
	}
	
	public double nextDouble() throws Exception {
		return Double.parseDouble(nextToken());
	}
}