Problem: You are given an integer n and an array a_1, a_2, …, a_n. You should reorder the elements of the array a in such way that the sum of MEX on prefixes (i-th prefix is a_1, a_2, …, a_i) is maximized.

Formally, you should find an array b_1, b_2, …, b_n, such that the sets of elements of arrays a and b are equal (it is equivalent to array b can be found as an array a with some reordering of its elements) and ∑_{i=1}^{n} MEX(b_1, b_2, …, b_i) is maximized.

MEX of a set of nonnegative integers is the minimal nonnegative integer such that it is not in the set.

For example, MEX(\{1, 2, 3\}) = 0, MEX(\{0, 1, 2, 4, 5\}) = 3.

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 100).

The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 100).

Output

For each test case print an array b_1, b_2, …, b_n — the optimal reordering of a_1, a_2, …, a_n, so the sum of MEX on its prefixes is maximized.

If there exist multiple optimal answers you can find any.

Example

Input


3
7
4 2 0 1 3 3 7
5
2 2 8 6 9
1
0


Output


0 1 2 3 4 7 3 
2 6 8 9 2 
0 

Note

In the first test case in the answer MEX for prefixes will be: 

  1. MEX(\{0\}) = 1 
  2. MEX(\{0, 1\}) = 2 
  3. MEX(\{0, 1, 2\}) = 3 
  4. MEX(\{0, 1, 2, 3\}) = 4 
  5. MEX(\{0, 1, 2, 3, 4\}) = 5 
  6. MEX(\{0, 1, 2, 3, 4, 7\}) = 5 
  7. MEX(\{0, 1, 2, 3, 4, 7, 3\}) = 5 

The sum of MEX = 1 + 2 + 3 + 4 + 5 + 5 + 5 = 25. It can be proven, that it is a maximum possible sum of MEX on prefixes.

Solution (in PYTHON):

Solution:


from __future__ import division, print_function

import os,sys
from io import BytesIO, IOBase

if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip


# sys.setrecursionlimit(10000000)


def dmain():
    sys.setrecursionlimit(1000000)
    threading.stack_size(1024000)
    thread = threading.Thread(target=main)
    thread.start()
    
#from collections import deque, Counter, OrderedDict,defaultdict
#from heapq import nsmallest, nlargest, heapify,heappop ,heappush, heapreplace
#from math import log,sqrt,factorial,cos,tan,sin,radians
#from bisect import bisect,bisect_left,bisect_right,insort,insort_left,insort_right
#from decimal import *
#import threading
#from itertools import permutations
#Copy 2D list  m = [x[:] for x in mark] .. Avoid Using Deepcopy

# abc='abcdefghijklmnopqrstuvwxyz'
# abd={'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12, 'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24, 'z': 25}
# mod=1000000007
# #mod=998244353
# inf = float("inf")
# vow=['a','e','i','o','u']
# dx,dy=[-1,1,0,0],[0,0,1,-1]
# def getKey(item): return item[1] 
# def sort2(l):return sorted(l, key=getKey,reverse=True)
# def d2(n,m,num):return [[num for x in range(m)] for y in range(n)]
# def isPowerOfTwo (x): return (x and (not(x & (x - 1))) )
# def decimalToBinary(n): return bin(n).replace("0b","")
# def ntl(n):return [int(i) for i in str(n)]
# def ncr(n,r): return factorial(n)//(factorial(r)*factorial(max(n-r,1)))

# def ceil(x,y):
#     if x%y==0:
#         return x//y
#     else:
#         return x//y+1

# def powerMod(x,y,p):
#     res = 1
#     x %= p
#     while y > 0:
#         if y&1:
#             res = (res*x)%p
#         y = y>>1
#         x = (x*x)%p
#     return res

# def gcd(x, y):
#     while y:
#         x, y = y, x % y
#     return x
    
def isPrime(n) : # Check Prime Number or not 
    if (n <= 1) : return False
    if (n <= 3) : return True
    if (n % 2 == 0 or n % 3 == 0) : return False
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return False
        i = i + 6
    return True

def lower_bound(l,k):
    s = 0
    e = len(l)
    while(s<e):
        m = (s+e-1)//2
        if(l[m] <= k):
            s = m+1
        else:
            e = m
    return s

def upper_bound(l,k):
    s = 0
    e = len(l)
    while(s<e):
        m = (s+e-1)//2
        if(l[m] >= k):
            e = m
        else:
            s = m+1
    return s

def bs(l,k):
    s = 0
    e = len(l) - 1
    while(s<=e):
        m = (s+e)//2
        if(l[m] == k):
            return m
        elif(l[m] > k):
            e = m-1
        else:
            s = m+1
    return -1


# l = [0]*1000001
# v = [0]*1000001
# d = [0]*1000001
# from queue import Queue
def bfs(n):
    v[n] = 1
    q = Queue()
    q.put(n)
    d[n] = 0
    while(not q.empty()):
        cur = q.get()
        # print(cur,v[:5],q)
        for i in l[cur]:
            if(v[i]==0):
                v[i] = 1
                d[i] = d[cur] + 1
                q.put(i)

def valid(a,b):
    c = 0
    while(a>0):
        if(a%10 == b%10):
            c += 1
        a = a//10
        b = b//10
    if(c==3):
        return True
    return False

col = [0]*1000001
def dfs(n,c):
    v[n] = 1
    col[n] = c
    for i in l[n]:
        if(v[i]==0):
            dfs(i, c)



def read():
    sys.stdin  = open('input.txt', 'r')  
    sys.stdout = open('output.txt', 'w') 


def ii():  return int(input())
def si():  return input()
def mi():  return map(int,input().strip().split(" "))
def msi(): return map(str,input().strip().split(" "))
def li():  return list(mi())





def main():
    # read()

    for _ in range(ii()):
        n = ii()
        l = li()
        d = {}
        for i in l:
            d[i] = d.get(i,0) + 1
        m = max(d.values())
        l = list(set(l))
        l.sort()
        for i in range(m):
            for j in l:
                if(d[j]):
                    print(j,end=" ")
                    d[j] -= 1
        print()









# region fastio
# template taken from https://github.com/cheran-senthil/PyRival/blob/master/templates/template.py

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()


if sys.version_info[0] < 3:
    sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)

input = lambda: sys.stdin.readline().rstrip("\r\n")

# endregion


if __name__ == "__main__":
    
    main()
    # dmain()

# Comment Read()