Problem: Permutation p is a sequence of integers p=[p_1, p_2, ..., p_n], consisting of n distinct (unique) positive integers between 1 and n, inclusive. For example, the following sequences are permutations: [3, 4, 1, 2], [1], [1, 2]. The following sequences are not permutations: [0], [1, 2, 1], [2, 3], [0, 1, 2].

The important key is in the locked box that you need to open. To open the box you need to enter secret code. Secret code is a permutation p of length n. 

You don't know this permutation, you only know the array q of prefix maximums of this permutation. Formally:

  * q_1=p_1, 
  * q_2=max(p_1, p_2), 
  * q_3=max(p_1, p_2,p_3), 
  * ... 
  * q_n=max(p_1, p_2,...,p_n). 



You want to construct any possible suitable permutation (i.e. any such permutation, that calculated q for this permutation is equal to the given array).

Input

The first line contains integer number t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.

The first line of a test case contains one integer n (1 ≤ n ≤ 10^{5}) — the number of elements in the secret code permutation p.

The second line of a test case contains n integers q_1, q_2, ..., q_n (1 ≤ q_i ≤ n) — elements of the array q for secret permutation. It is guaranteed that q_i ≤ q_{i+1} for all i (1 ≤ i < n).

The sum of all values n over all the test cases in the input doesn't exceed 10^5.

Output

For each test case, print:

  * If it's impossible to find such a permutation p, print "-1" (without quotes). 
  * Otherwise, print n distinct integers p_1, p_2, ..., p_n (1 ≤ p_i ≤ n). If there are multiple possible answers, you can print any of them. 

Example

Input


4
5
1 3 4 5 5
4
1 1 3 4
2
2 2
1
1


Output


1 3 4 5 2 
-1
2 1 
1 

Note

In the first test case of the example answer [1,3,4,5,2] is the only possible answer:

  * q_{1} = p_{1} = 1; 
  * q_{2} = max(p_{1}, p_{2}) = 3; 
  * q_{3} = max(p_{1}, p_{2}, p_{3}) = 4; 
  * q_{4} = max(p_{1}, p_{2}, p_{3}, p_{4}) = 5; 
  * q_{5} = max(p_{1}, p_{2}, p_{3}, p_{4}, p_{5}) = 5. 



It can be proved that there are no answers for the second test case of the example.

Solution (in PYTHON3):

Solution:
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 #     #    #   #          #        #       # #     #    #     #      #   #     ###  
 #     #   #     #        #         #       #  #    #   #       #    #     #    ###  
 ######   #########      #          #       #   #   #   #           #########    #   
 ######   #########     #           #       #    #  #   #           #########    #   
 #     #  #       #    #            #       #     # #   #    ####   #       #    #   
 #     #  #       #   #             #       #      ##   #    #  #   #       #        
 ######   #       #  #######     #######    #       #    #####  #   #       #    #   
 
from __future__ import print_function # for PyPy2
# from itertools import permutations
# from functools import cmp_to_key  # for adding custom comparator
# from fractions import Fraction
from collections import *
from sys import stdin
import sys
# from bisect import *
from heapq import *
from math import log2, ceil, sqrt, gcd, log
 
g   = lambda : stdin.readline().strip()
gl  = lambda : g().split()
gil = lambda : [int(var) for var in gl()]
gfl = lambda : [float(var) for var in gl()]
gcl = lambda : list(g())
gbs = lambda : [int(var) for var in g()]
rr = lambda x : reversed(range(x)) 
mod = int(1e9)+7
inf = float("inf")
# range = xrange

t, = gil()

for _ in range(t):
    n, = gil()
    a = gil()
    ans = [None]*n
    left = set(range(1, n+1))
    left.remove(a[0])
    ans[0] = a[0]

    for i in range(1, n):
        if a[i] != a[i-1]:
            ans[i] = a[i]
            if ans[i] in left:left.remove(ans[i])
    

    left = list(left)
    left.sort(reverse=True)

    for i in range(n):
        if ans[i] == None:
            if left:ans[i] = left.pop()

    # print(ans, a)
    if None in ans:
        print(-1)
    else:
        maxi = 0
        for i in range(n):
            maxi = max(maxi, ans[i])
            if a[i] != maxi:
                break

        if a[i] == maxi:
            print(*ans)
        else:
            print(-1)