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 PYTHON3):

Solution:
import sys
from collections import defaultdict
import math
from heapq import *
import itertools

MAXNUM = math.inf
MINNUM = -1 * math.inf
ASCIILOWER = 97
ASCIIUPPER = 65

pq = []  # list of entries arranged in a heap
entry_finder = {}  # mapping of tasks to entries
REMOVED = "<removed-task>"  # placeholder for a removed task
counter = itertools.count()  # unique sequence count


def add_task(task, priority=0):
    "Add a new task or update the priority of an existing task"
    if task in entry_finder:
        remove_task(task)
    count = next(counter)
    entry = [priority, count, task]
    entry_finder[task] = entry
    heappush(pq, entry)


def remove_task(task):
    "Mark an existing task as REMOVED.  Raise KeyError if not found."
    entry = entry_finder.pop(task)
    entry[-1] = REMOVED


def pop_task():
    "Remove and return the lowest priority task. Raise KeyError if empty."
    while pq:
        priority, count, task = heappop(pq)
        if task is not REMOVED:
            del entry_finder[task]
            return task
    raise KeyError("pop from an empty priority queue")


def getInt():
    return int(sys.stdin.readline().rstrip())


def getInts():
    return map(int, sys.stdin.readline().rstrip().split(" "))


def getString():
    return sys.stdin.readline().rstrip()


def printOutput(ans):
    sys.stdout.write("%.15f" % (ans))


def findParent(a, parents):

    cur = a
    while parents[cur] != cur:
        cur = parents[cur]

    parents[a] = cur  # reduction of search time on next search
    return cur


def union(a, b, parents):

    parents[b] = a


def solve(nodeList, edgeList, edgeHeap):
    parents = [i for i in range(nodeList)]

    minTreeEdges = []
    totalEdges = defaultdict(int)

    # Get min spanning tree
    while edgeHeap:
        eVal, n1, n2 = heappop(edgeHeap)
        n1Parent = findParent(n1, parents)
        n2Parent = findParent(n2, parents)
        if n1Parent != n2Parent:
            union(n1Parent, n2Parent, parents)
            totalEdges[n1] += 1
            totalEdges[n2] += 1
            add_task(n1, totalEdges[n1])
            add_task(n2, totalEdges[n2])

            minTreeEdgeList[n1] = (n2, eVal)
            minTreeEdgeList[n2] = (n1, eVal)

    # prune min spanning tree starting from leaves


def readinput():
    heap = []
    v, e = getInts()
    nodes = [0] + list(getInts()) 
    mx = 0
    for i in range(e):
        n1, n2, e = getInts()
        mx = max(mx, (nodes[n1] + nodes[n2]) / e)
    printOutput(mx)

readinput()