Tired of the overpopulated world, Miu - The introverted cat visits a new continent in search for a new house.  
There are $N$ houses lying on the X-axis.

Their positions are given by $X$$i$ , where $i$ refers to the $i$th house. ( $1 <= i <= N$ )

Each of these positions are pairwise distinct 
Miu is supposed to choose one of these houses for herself.

Miu defines a term - The Distance of Peace,  as the minimum distance from her house to any other house.  
Miu wonders what is maximum Distance of Peace she can obtain. Can you help her?

-----Input:-----
- The first line of the input consists of a single integer $T$, denoting the number of test cases  
- The first line of each test case consists of a single integer $N$ 
- The second line of each test case consists of $N$ space-separated integers
$X$$1$ $X$$2$ $X$$3$ … $X$$N$

-----Output:-----
- For each test case print the answer in a single line, the maximum Distance of Peace Miu can obtain

-----Constraints-----
- 1 <= $T$ <= 100  
- 2 <= $N$ <= 105 
- -109 <= $X$$i$ <= 109 
- Sum of $N$ over all test cases does not exceed 106 

-----Subtasks-----
Subtask #1 (30 points): 
- $N$ <= 103 
Subtask #2 (70 points): 
- Original Constraints

-----Sample Input:-----
2

6

7 -1 2 13 -5 15

4

6 10 3 12  

-----Sample Output:-----
5

3  

-----EXPLANATION:-----
Test Case 1:

The $1$st house has the maximum Distance of Peace, which is from the $3$rd house:
$| 7 - 2 | = 5$

Hence, the answer is $5$

```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 = "for _ in range(int(input())):\n n = int(input())\n a = sorted(map(int, input().split()))\n\n maxi = float('-inf')\n\n for i in range(n):\n  mini = float('inf')\n\n  if i - 1 >= 0:\n   mini = min(mini, abs(a[i] - a[i-1]))\n\n  if i + 1 < n:\n   mini = min(mini, abs(a[i+1] - a[i]))\n\n  maxi = max(maxi, mini)\n\n print(maxi)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13267