Masha and Grisha like studying sets of positive integers.

One day Grisha has written a set A containing n different integers a_{i} on a blackboard. Now he asks Masha to create a set B containing n different integers b_{j} such that all n^2 integers that can be obtained by summing up a_{i} and b_{j} for all possible pairs of i and j are different.

Both Masha and Grisha don't like big numbers, so all numbers in A are from 1 to 10^6, and all numbers in B must also be in the same range.

Help Masha to create the set B that satisfies Grisha's requirement.


-----Input-----

Input data contains multiple test cases. The first line contains an integer t — the number of test cases (1 ≤ t ≤ 100).

Each test case is described in the following way: the first line of the description contains one integer n — the number of elements in A (1 ≤ n ≤ 100).

The second line contains n integers a_{i} — the elements of A (1 ≤ a_{i} ≤ 10^6). 


-----Output-----

For each test first print the answer:   NO, if Masha's task is impossible to solve, there is no way to create the required set B.  YES, if there is the way to create the required set. In this case the second line must contain n different positive integers b_{j} — elements of B (1 ≤ b_{j} ≤ 10^6). If there are several possible sets, output any of them. 


-----Example-----
Input
3
3
1 10 100
1
1
2
2 4

Output
YES
1 2 3 
YES
1 
YES
1 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 = '\'\'\'\nfrom random import randint\n\nvisited = [-1] * (2 * 10 ** 6 + 1)\nt = int(input())\nfor i in range(t):\n    n, A = int(input()), list(map(int, input().split()))\n    A.sort()\n    res = [1] * n\n    v = 1\n    cnt = 0\n    while cnt < n:\n        #v = randint(1, 10**6)\n        if all(visited[a + v] != i for a in A):\n            for a in A:\n                visited[a + v] = i\n            res[cnt] = v\n            cnt += 1\n        v += 1\n    print("YES\\n" + \' \'.join(map(str,res)))\n\'\'\'\n\nt = int(input())\n\ndef check(arr,v,dic):\n    for i in arr:\n        if dic[i+v] == 1:\n            return True\n    return False\n\n\ndef check2(arr,v,dic):\n    ok = False\n    for i in arr:\n        if dic[i+v] == 1:\n            ok = True\n            break\n    return ok\n\n\ndef check3(arr,v,dic):\n    return any(dic[a + v] == 1 for a in arr)\n\n\ndic = [0]*2000005\n\nfor _ in range(t):\n    n = int(input())\n    arr = list(map(int,input().split()))\n    arr.sort()\n    brr = [1]*n\n    cnt = 0\n    i = 1\n    flag = True\n    tmp = {}\n    while cnt < n:\n        \'\'\'\n        while check(arr,i,dic):\n            i += 1\n        brr[cnt] = i\n\n        for v in arr:\n            #if i+v>2e6:\n            #    break\n            dic[i+v] = 1\n            tmp[i+v] = 1\n        cnt += 1\n        \'\'\'\n        #while any(dic[a + i] != 0 for a in arr):\n        #    i += 1\n\n        #while check3(arr, i, dic):\n        #    i += 1\n\n        ok = True\n        for a in arr:\n            if dic[a + i] == 1:\n                ok = False\n                break\n\n        if not ok:\n            i += 1\n            continue\n\n        for a in arr:\n            dic[a + i] = 1\n            tmp[a + i] = 1\n        brr[cnt] = i\n        cnt += 1\n        i += 1\n    if flag:\n        print("YES")\n        print(" ".join(map(str,brr)))\n    else:\n        print("NO")\n    for k in list(tmp.keys()):\n        dic[k] = 0\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 16007042