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: $\left\{\begin{array}{ll}{\frac{v}{e}} & {(e > 0)} \\{0} & {(e = 0)} \end{array} \right.$ 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:  $V^{\prime} \subseteq V$;  edge $(a, b) \in E^{\prime}$ if and only if $a \in V^{\prime}, b \in V^{\prime}$, and edge $(a, b) \in E$;  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), $m(0 \leq m \leq \frac{n(n - 1)}{2})$. 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 x_{i} (1 ≤ x_{i} ≤ 10^6), where x_{i} 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 a_{i}, b_{i}, c_{i} (1 ≤ a_{i} < b_{i} ≤ n; 1 ≤ c_{i} ≤ 10^3), denoting an edge between node a_{i} and b_{i} with value c_{i}. 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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "a = input().split(' ')\nn = int(a[0])\nm = int(a[1])\nb = input().split(' ')\na.clear()\nfor i in range(0, n) :\n    a.append(int(b[i]))\nans = 0\nfor i in range(0, m) :\n    b = input().split(' ')\n    c = []\n    for j in range(0, 3) : \n        c.append(int(b[j]))\n    ans = max(ans, (a[c[0] - 1] + a[c[1] - 1]) / c[2])\nprint(ans)\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13393