You are given a sequence of integers $A_1, A_2, \dots, A_N$.
You should choose an arbitrary (possibly empty) subsequence of $A$ and multiply each element of this subsequence by $-1$. The resulting sequence should satisfy the following condition: the sum of elements of any contiguous subsequence with length greater than 1 is strictly positive.
You should minimise the sum of elements of the resulting sequence. Find one such sequence with the minimum possible sum.

-----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 $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \dots, A_N$.

-----Output-----
For each test case, print a single line containing $N$ space-separated integers $B_1, B_2, \dots, B_N$. For each valid $i$, $B_i$ must be equal to either $A_i$ (the sign of this element did not change) or $-A_i$ (the sign of this element changed).
If there is more than one answer, you may output any one.

-----Constraints-----
- $1 \le T \le 10^5$
- $2 \le N \le 10^5$
- $1 \le A_i \le 10^9$ for each valid $i$
- the sum of $N$ for all test cases does not exceed $5 \cdot 10^5$

-----Subtasks-----
Subtask #1 (20 points):
- $1 \le T \le 200$
- $2 \le N \le 10$
Subtask #2 (30 points):
- $1 \le T \le 1,000$
- $N \le 2,000$
Subtask #3 (50 points): original constraints

-----Example Input-----
4
4
4 3 1 2
6
1 2 2 1 3 1
5
10 1 2 10 5
4
1 2 1 2

-----Example Output-----
4 3 -1 2
-1 2 2 -1 3 -1
10 -1 2 10 -5
1 2 -1 2

-----Explanation-----
Example case 1: If we change only the sign of $A_3$, we get a sequence $\{4, 3, -1, 2\}$ with sum $8$. This sequence is valid because the sums of all its contiguous subsequences with length $> 1$ are positive. (For example, the sum of elements of the contiguous subsequence $\{A_3, A_4\}$ equals $-1 + 2 = 1 > 0$.)
There are only two valid sequences $\{4, 3, -1, 2\}$ and $\{4, 3, 1, 2\}$ with sums $8$ and $10$ respectively, so this sequence has the smallest possible sum.
For instance, the sequence $\{4, -3, 1, 2\}$ isn't valid, because the sum of $\{A_2, A_3, A_4\}$ equals $-3 + 1 + 2 = 0 \le 0$.

```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 = '"""\n4\n4\n4 3 1 2\n6\n1 2 2 1 3 1\n5\n10 1 2 10 5\n4\n1 2 1 2\n"""\ntests = int(input())\n\nfor _ in range(tests):\n\n n = int(input())\n ls = list(map(int, input().split()))\n\n if ls[0] < ls[1]:\n  ls[0] = -ls[0]\n\n if ls[-1] < ls[-2]:\n  ls[-1] = -ls[-1]\n\n for i in range(1, n - 1):\n  if ls[i] < ls[i - 1] and ls[i] < ls[i + 1]:\n   ls[i] = -ls[i]\n   \'\'\'\n      if i > 1 and ls[i - 2] < 0 and ls[i] - ls[i-2] >= ls[i-1]:\n       # There can be only one!\n       if -ls[i-2] < ls[i]:\n        # We win!\n        ls[i-2] = -ls[i-2]\n        ls[i] = -ls[i]\n        #else:\n        # They win!\n        # Do nothing\n      else:\n       # We both can go negative\n       ls[i] = -ls[i]\n      \'\'\'\n   \n #print(ls)\n \n ind = 1\n\n while ind < n - 1:\n\n  started = False\n  pos = []\n  while ind < n - 1 and ls[ind] + ls[ind - 1] + ls[ind + 1] <= 0:\n   if not started:\n    pos.append(ind - 1)\n    pos.append(ind + 1)\n    started = True\n   else:\n    pos.append(ind + 1)\n   ind += 2\n\n  #print(pos,ls)\n\n  if started:\n   rec = [0] * (len(pos) + 1)\n\n   for i in pos:\n    ls[i] = -ls[i]\n\n   rec[0] = 0\n   rec[1] = ls[pos[0]]\n\n   for i in range(2, len(pos) + 1):\n    rec[i] = max(rec[i - 1], ls[pos[i - 1]] + rec[i - 2])\n\n   itr = len(pos)\n   while itr > 0:\n    if itr == 1 or rec[itr] == ls[pos[itr - 1]] + rec[itr - 2]:\n     ls[pos[itr - 1]] = -ls[pos[itr - 1]]\n     itr -= 2\n    else:\n     itr -= 1\n\n  ind += 1\n\n for i in ls:\n  print(i, end = \' \')\n print() \n\n  \n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14173