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.

Difficulty: MEDIUM_HARD
Tags: Mathematics

Greedy algorithms
Skill types: Greedy algorithms

Starter code:

Solutions:
(n, m) = map(int, input().split())
v = list(map(int, input().split()))
mini = 0
for i in range(m):
	(a, b, c) = map(int, input().split())
	mini = max(mini, (v[a - 1] + v[b - 1]) / c)
print(mini)


(n, m) = input().split()
a = [0] + list(map(float, input().split()))
ans = 0
for _ in range(int(m)):
	(u, v, c) = input().split()
	ans = max(ans, (a[int(u)] + a[int(v)]) / float(c))
print(ans)


(n, m) = map(int, input().split())
a = list(map(int, input().split()))
ret = 0.0
for i in range(m):
	(x, y, c) = map(int, input().split())
	ret = max(ret, (a[x - 1] + a[y - 1]) / c)
print(ret)


(nodes, edges) = map(int, input().split())
x = list(map(int, input().split()))
error = 0
for i in range(edges):
	(a, b, c) = map(int, input().split())
	error = max(error, (x[a - 1] + x[b - 1]) / c)
print(error)


(n, m) = map(int, input().split())
x = [int(c) for c in input().split()]
ans = 0
for _ in range(m):
	(a, b, c) = map(int, input().split())
	ans = max(ans, (x[a - 1] + x[b - 1]) / c)
print(ans)


(nodes, edges) = map(int, input().split())
nodesValues = list(map(int, input().split()))
density = 0
total = 0
for i in range(edges):
	(node1, node2, edgeValue) = map(int, input().split())
	total = (nodesValues[node2 - 1] + nodesValues[node1 - 1]) / edgeValue
	if total > density:
		density = total
print(density)


(n, m) = map(int, input().split(' '))
val = list(map(int, input().split(' ')))
ans = 0
for i in range(m):
	(x, y, z) = map(int, input().split(' '))
	ans = max(ans, (val[x - 1] + val[y - 1]) / z)
print(ans)


from sys import stdin
input = stdin.readline
(n, m) = map(int, input().split())
arr = [int(i) for i in input().split()]
res = 0.0
for _ in range(m):
	(a, b, c) = map(int, input().split())
	if c:
		res = max(res, (arr[a - 1] + arr[b - 1]) / c)
print(res)


import sys
f = sys.stdin
(n, m) = map(int, f.readline().strip().split())
v = [int(u) for u in f.readline().strip().split()]
d = [{} for u in range(n)]
for i in range(m):
	(xi, yi, ei) = map(int, f.readline().strip().split())
	d[yi - 1][xi - 1] = ei
	d[xi - 1][yi - 1] = ei

def ff(i, s):
	for k in d[i]:
		if rt[k] == 0:
			rt[k] = s
			dlist[k] = 1
			ff(k, s)
s = 0
rt = [0 for u in range(n)]
glist = []
for i in range(n):
	if rt[i] == 0:
		s += 1
		dlist = {}
		rt[i] = s
		dlist[i] = 1
		ff(i, s)
		glist.append(dlist)
roMax = 0.0
t_ro = 0.0
ro = 0.0
for g in glist:
	if len(g) > 1:
		for gi in g:
			for u in d[gi]:
				if u in g:
					t_ro = (v[gi] + v[u]) / d[gi][u]
					if t_ro > ro:
						ro = t_ro
						graf = [gi, u]
print(ro)


import math

def solve():
	(n, m) = [int(i) for i in input().split()]
	vw = [int(i) for i in input().split()]
	M = 0.0
	for _ in range(m):
		(a, b, c) = [int(i) for i in input().split()]
		M = max(M, (vw[a - 1] + vw[b - 1]) / c)
	print(M)
solve()


import sys

def input():
	return sys.stdin.readline().strip()
(n, m) = map(int, input().split())
x = [int(i) for i in input().split()]
edge = []
val = 0
for i in range(m):
	(a, b, c) = map(int, input().split())
	val = max((x[a - 1] + x[b - 1]) / c, val)
print(val)


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 = []
entry_finder = {}
REMOVED = '<removed-task>'
counter = itertools.count()

def add_task(task, priority=0):
	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):
	entry = entry_finder.pop(task)
	entry[-1] = REMOVED

def pop_task():
	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
	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)
	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)

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()