You are given a set $S$ and $Q$ queries. Initially, $S$ is empty. In each query:
- You are given a positive integer $X$.
- You should insert $X$ into $S$.
- For each $y \in S$ before this query such that $y \neq X$, you should also insert $y \oplus X$ into $S$ ($\oplus$ denotes the XOR operation).
- Then, you should find two values $E$ and $O$: the number of elements of $S$ with an even number of $1$-s and with an odd number of $1$-s in the binary representation, respectively.
Note that a set cannot have duplicate elements, so if you try to insert into $S$ an element that is already present in $S$, then nothing happens.

-----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 each test case contains a single integer $Q$.
- Each of the next $Q$ lines contains a single integer $X$ describing a query.

-----Output-----
For each query, print a single line containing two space-separated integers $E$ and $O$.

-----Constraints-----
- $1 \le T \le 5$
- $1 \le Q, X \le 10^5$

-----Subtasks-----
Subtask #1 (30 points):
- $1 \le Q \le 1,000$
- $1 \le X \le 128$
Subtask #2 (70 points): original constraints

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

-----Example Output-----
0 1
1 2
3 4

-----Explanation-----
Example case 1:
- Initially, the set is empty: $S = \{\}$.
- After the first query, $S = \{4\}$, so there is only one element with an odd number of $1$-s in the binary representation ("100").
- After the second query, $S = \{4,2,6\}$, there is one element with an even number of $1$-s in the binary representation ($6$ is "110") and the other two elements have an odd number of $1$-s.
- After the third query, $S = \{4,2,6,7,3,5,1\}$.

```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 = 'T = int(input())\nfor a in range(T):\n Q = int(input())\n l2 = []\n even = 0\n odd = 0\n for _ in range(Q):\n\n  l3 =[]\n  z = int(input())\n  if z not in l2:\n   x = str(bin(z))\n\n   if (x.count(\'1\') % 2) == 0:\n    even += 1\n   else:\n    odd += 1\n   for w in l2:\n    l3.append(w ^ z)\n    x = str(bin(w ^ z))\n\n    if (x.count(\'1\') % 2) == 0:\n     even += 1\n    else:\n     odd += 1\n   l2.append(z)\n   l2.extend(l3)\n\n  print(even,end = " ")\n  print(odd)\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13377