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.util.*;
import java.io.*;

/*
 * author:yanghui
 */
public class C {

	class FastIO {
		BufferedReader br;
		StringTokenizer st;
		PrintWriter out;

		public FastIO(File in, File o) {
			try {
				br = new BufferedReader(new FileReader(in));
				out = new PrintWriter(new FileWriter(o));
			} catch (Exception e) {
				br = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(new OutputStreamWriter(System.out));
			}
			eat("");
		}

		public FastIO() {
			br = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(new OutputStreamWriter(System.out));
			eat("");
		}

		public void eat(String s) {
			st = new StringTokenizer(s);
		}

		public String nextLine() {
			try {
				return br.readLine();
			} catch (IOException e) {
				throw new IOError(e);
			}
		}

		public boolean hasNext() {
			while (!st.hasMoreTokens()) {
				String s = nextLine();
				if (s == null)
					return false;
				eat(s);
			}
			return true;
		}

		public String next() {
			hasNext();
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public void print(String ans) {
			out.print(ans);
			out.flush();
		}

		public void print(int ans) {
			out.print(ans);
			out.flush();
		}

		public void print(long ans) {
			out.print(ans);
			out.flush();
		}

		public void print(double ans) {
			out.print(ans);
			out.flush();
		}

		public void println(String ans) {
			out.println(ans);
			out.flush();
		}

		public void println(int ans) {
			out.println(ans);
			out.flush();
		}

		public void println(long ans) {
			out.println(ans);
			out.flush();
		}

		public void println(double ans) {
			out.println(ans);
			out.flush();
		}

		public void println() {
			println("");
			out.flush();
		}

		public void printf(String arg0, Object... arg1) {
			out.printf(arg0, arg1);
			out.flush();
		}

		public void println(int[] ans) {
			for (int i = 0; i < ans.length; i++)
				print(ans[i] + " ");
			println();
		}

		public void println(long[] ans) {
			for (int i = 0; i < ans.length; i++)
				print(ans[i] + " ");
			println();
		}

		public void println(double[] ans) {
			for (int i = 0; i < ans.length; i++)
				print(ans[i] + " ");
			println();
		}

		public void println(Object... ans) {
			for (Object cur : ans)
				print(cur.toString() + " ");
			println();
		}

		public void println(Object ans[][]) {
			for (int i = 0; i < ans.length; i++) {
				println(ans[i]);
			}
		}

		public void println(int ans[][]) {
			for (int i = 0; i < ans.length; i++) {
				println(ans[i]);
			}
		}

		public void println(long ans[][]) {
			for (int i = 0; i < ans.length; i++) {
				println(ans[i]);
			}
		}

		public void println(double ans[][]) {
			for (int i = 0; i < ans.length; i++) {
				println(ans[i]);
			}
		}

		public void println(List<Object> ans) {
			for (Object i : ans) {
				print(i.toString() + " ");
			}
			println();
		}

		public void close() {
			out.flush();
			out.close();
		}
	}

	public static class ArrayUtils {
		public static void shuffleArray(int a[]) {
			int n = a.length;
			Random rnd = new Random();
			for (int i = 0; i < n; ++i) {
				int tmp = a[i];
				int randomPos = i + rnd.nextInt(n - i);
				a[i] = a[randomPos];
				a[randomPos] = tmp;
			}
		}

		public static void shuffleArray(long a[]) {
			int n = a.length;
			Random rnd = new Random();
			for (int i = 0; i < n; ++i) {
				long tmp = a[i];
				int randomPos = i + rnd.nextInt(n - i);
				a[i] = a[randomPos];
				a[randomPos] = tmp;
			}
		}

		public static void shuffleArray(double a[]) {
			int n = a.length;
			Random rnd = new Random();
			for (int i = 0; i < n; ++i) {
				double tmp = a[i];
				int randomPos = i + rnd.nextInt(n - i);
				a[i] = a[randomPos];
				a[randomPos] = tmp;
			}
		}

		public static void shuffleArray(float a[]) {
			int n = a.length;
			Random rnd = new Random();
			for (int i = 0; i < n; ++i) {
				float tmp = a[i];
				int randomPos = i + rnd.nextInt(n - i);
				a[i] = a[randomPos];
				a[randomPos] = tmp;
			}
		}

	}

	FastIO scan = new FastIO(new File("in"), new File("out"));

	// FastIO scan = new FastIO();

	public void run() {

		int n = scan.nextInt();
		int m = scan.nextInt();
		int v1[] = new int[n+1];
		for(int i = 1 ; i <= n; i ++)
			v1[i] = scan.nextInt();
		double ans = 0;
		for(int i = 0 ; i < m ; i ++){
			int s = scan.nextInt();
			int t = scan.nextInt();
			int v = scan.nextInt();
			ans = Math.max(ans, (double)(v1[s] + v1[t])/(double)v);
		}
		scan.println(ans);
		
		scan.close();
	}

	public static void main(String args[]) throws Exception {
		new C().run();
	}
}