Consider the infinite sequence $s$ of positive integers, created by repeating the following steps:

  Find the lexicographically smallest triple of positive integers $(a, b, c)$ such that   $a \oplus b \oplus c = 0$, where $\oplus$ denotes the bitwise XOR operation.  $a$, $b$, $c$ are not in $s$.  Here triple of integers $(a_1, b_1, c_1)$ is considered to be lexicographically smaller than triple $(a_2, b_2, c_2)$ if sequence $[a_1, b_1, c_1]$ is lexicographically smaller than sequence $[a_2, b_2, c_2]$.  Append $a$, $b$, $c$ to $s$ in this order.  Go back to the first step. 

You have integer $n$. Find the $n$-th element of $s$.

You have to answer $t$ independent test cases.

A sequence $a$ is lexicographically smaller than a sequence $b$ if in the first position where $a$ and $b$ differ, the sequence $a$ has a smaller element than the corresponding element in $b$.


-----Input-----

The first line contains a single integer $t$ ($1 \le t \le 10^5$) — the number of test cases.

Each of the next $t$ lines contains a single integer $n$ ($1\le n \le 10^{16}$) — the position of the element you want to know.


-----Output-----

In each of the $t$ lines, output the answer to the corresponding test case.


-----Example-----
Input
9
1
2
3
4
5
6
7
8
9

Output
1
2
3
4
8
12
5
10
15



-----Note-----

The first elements of $s$ are $1, 2, 3, 4, 8, 12, 5, 10, 15, \dots $

```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 = 'import sys\ninput = sys.stdin.readline\nt = int(input())\ns = [int(input()) for i in range(t)]\nres = []\nfor num in s:\n    num -= 1\n    mod = num % 3\n    num = num // 3\n    div = 1\n    while True:\n        if num // div != 0:\n            num -= div\n            div *= 4\n        else:\n            break\n    a = div + num\n    b = a * 2\n    tmp = a\n    coff = 1\n    while True:\n        if tmp == 0:\n            break\n        if tmp % 4 == 2:\n            b -= coff\n        if tmp % 4 == 3:\n            b -= coff * 5\n        tmp = tmp // 4\n        coff *= 4\n    c = a ^ b\n    if mod == 0:\n        print(a)\n    if mod == 1:\n        print(b)\n    if mod == 2:\n        print(c)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13225