There are $N$ cities on a circle, numbered $1$ through $N$. For each $i$ ($1 \le i \le N-1$), cities $i$ and $i+1$ are directly connected by a bidirectional road with length $A_i$, and cities $N$ and $1$ are also directly connected by a bidirectional road with length $A_N$. However, we do not know the lengths of some roads.
For each city $i$, we do know that it has an opposite city — formally, there is a city $j \neq i$ such that the clockwise distance between cities $i$ and $j$ is equal to the counterclockwise distance between these cities.
Please find the lengths of all roads in such a way that the above condition is satisfied and the sum of lengths of all roads is minimised.

-----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 $A_1, A_2, \dots, A_N$. For each valid $i$, $A_i = -1$ denotes that the length of road $i$ is unknown.

-----Output-----
For each test case, print a line containing the string "NO" if there is no solution or "YES" otherwise. If a solution exists, print a second line containing $N$ space-separated positive integers — the lengths of all roads in your solution. Each of these integers should be $\le 10^9$. If there are multiple solutions, you may print any one.

-----Constraints-----
- $1 \le T \le 100$
- $3 \le N \le 10^5$
- $1 \le A_i \le 10^9$ or $A_i = -1$ for each valid $i$
- the sum of $N$ for all test cases does not exceed $3\cdot 10^5$

-----Subtasks-----
Subtask #1 (10 points): $N \le 4$
Subtask #2 (20 points): $A_i = \pm 1$ for each valid $i$
Subtask #3 (70 points): original constraints

-----Example Input-----
4
4
1 1 1 1
4
1 1 1 2
4
1 -1 -1 4
4
1 -1 2 -1

-----Example Output-----
YES
1 1 1 1
NO
YES
1 4 1 4
NO

```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 z in range(t):\n n=int(input())\n a=[int(x) for x in input().split()]\n flag=0\n if n%2==0 and (n//2)%2==0:     \n  for i in range(n-n//2):\n   if a[i]!=-1 and a[i+n//2]!=-1 and a[i+n//2]!=a[i]:\n    flag=1\n    break\n   elif a[i]!=-1 and a[i+n//2]==-1:\n    a[i+n//2]=a[i]\n   elif a[i]==-1 and a[i+n//2]==-1:\n    a[i]=1\n    a[i+n//2]=1\n   elif a[i]==-1 and a[i+n//2]!=-1:\n    a[i]=a[i+n//2]\n elif n%2==0:\n  k=1\n  for i in a:\n   if i!=-1:\n    k=i\n  for i in range(n-n//2):\n   if a[i]!=-1 and a[i+n//2]!=-1 and a[i+n//2]!=a[i]:\n    flag=1\n    break\n   elif a[i]!=-1 and a[i+n//2]==-1:\n    a[i+n//2]=a[i]\n   elif a[i]==-1 and a[i+n//2]==-1:\n    a[i]=k\n    a[i+n//2]=k\n   elif a[i]==-1 and a[i+n//2]!=-1:\n    a[i]=a[i+n//2]\n else:\n  print("NO")\n  continue\n if sum(a)%2!=0:\n  flag=1\n if flag==0:\n  print("YES")\n  for i in a:\n   print(i,end=" ")\n  print()\n else:\n  print("NO")\n  \n   \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14077