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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/**
 *
 *
 * 10 5 8 1 10 3 6 2 9 7 4 4 2 6 3 1 9 10 5 8 7
 *
 * @author pttrung
 */
public class C {

    //   public static long x, y, gcd;
    public static int Mod = 1000000007;
    public static PrintWriter out;

    public static void main(String[] args) throws FileNotFoundException {
        Scanner in = new Scanner();
        out = new PrintWriter(System.out);
        //   System.out.println(Integer.MAX_VALUE);
        //PrintWriter out = new PrintWriter(new FileOutputStream(new File("output.txt")));
        int n = in.nextInt();
        int m = in.nextInt();
        int []data = new int[n];        
        for(int i = 0; i < n; i++){
            data[i] = in.nextInt();
        }
        double result = 0;
        for(int i = 0; i < m; i++){
            int a = in.nextInt() - 1;
            int b = in.nextInt() - 1;
            result = Math.max(result, (double)(data[a] + data[b])/in.nextInt());
        }
        out.println(result);
        out.close();
    }

    public static boolean add(int length, Node pa, StringBuilder builder) {
        if (length == 0) {
            pa.full = true;
            return true;
        }
        if (!pa.full) {
            if (pa.zero == null || !pa.zero.full) {
                if (pa.zero == null) {
                    pa.zero = new Node();
                }
                builder.append(0);
                add(length - 1, pa.zero, builder);
            } else {
                if (pa.one == null) {
                    pa.one = new Node();
                }
                builder.append(1);
                add(length - 1, pa.one, builder);
            }
            pa.full = (pa.zero != null && pa.zero.full) && (pa.one != null && pa.one.full);
            return true;
        }
        return false;
    }

    public static class Node {

        boolean full = false;
        Node zero, one;
    }

    public static long pow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val;
        } else {
            return val * val * a;
        }
    }

    public static int gcd(int a, int b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);


    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Point o) {
            if (x != o.x) {
                return x - o.x;
            } else {
                return y - o.y;
            }
        }
    }
//    public static void extendEuclid(long a, long b) {
//        if (b == 0) {
//            x = 1;
//            y = 0;
//            gcd = a;
//            return;
//        }
//        extendEuclid(b, a % b);
//        long x1 = y;
//        long y1 = x - (a / b) * y;
//        x = x1;
//        y = y1;
//
//    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}