You are given a sequence of non-negative integers $A_1, A_2, \ldots, A_N$. At most once, you may choose a non-negative integer $X$ and for each valid $i$, change $A_i$ to $A_i \oplus X$ ($\oplus$ denotes bitwise XOR).
Find the minimum possible value of the sum of all elements of the resulting sequence.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of the input contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output-----
For each test case, print a single line containing one integer ― the minimum possible sum.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10^5$
- $1 \le A_i \le 10^9$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (50 points):
- $1 \le N \le 10^3$
- $1 \le A_i \le 10^3$ for each valid $i$
Subtask #2 (50 points): original constraints

-----Example Input-----
3
5
2 3 4 5 6
4
7 7 7 7
3
1 1 3

-----Example Output-----
14
0
2

-----Explanation-----
Example case 1: If we choose $X = 6$, the sequence becomes $(4, 5, 2, 3, 0)$.
Example case 2: We can choose $X = 7$ to make all elements of the resulting sequence equal to $0$.
Example case 3: We can choose $X = 1$. The sequence becomes $(0, 0, 2)$, with sum $2$.

```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 = "\n\ndef solve():\n twopow = {}\n for i in range(31):twopow[i] = 2**i\n for _ in range(int(input())):\n  n = int(input())\n  a = list(map(int, input().split()))\n  b = dict()\n  for i in range(31):b[i] = 0\n  original_tot = 0\n  for i in range(n):\n   s = bin(a[i])[2:]\n   s = s[::-1]\n   original_tot += a[i]\n   for i in range(len(s)):\n    if s[i] == '1':\n     b[i] += 1\n  change = 0\n  for x in b:\n   p = b[x]\n   if p > 0:\n    if p > n - p:\n     change += (p - (n - p)) * (twopow[x])\n\n  original_tot -= change\n  print(original_tot)\n\nsolve()\n\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15837