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:
ll=lambda:map(int,input().split())
t=lambda:int(input())
ss=lambda:input()
#from math import log10 ,log2,ceil,factorial as f,gcd
#from itertools import combinations_with_replacement as cs 
#from functools import reduce
#from bisect import bisect_right as br,bisect_left as bl
#from collections import Counter
from math import inf,log,ceil


for _ in range(t()):
    n=t()
    a=list(ll())

    p=[a[0]]
    se=sorted(set(range(1,n+1)).difference(set(a)))
    i=1;
    while i<n:
        if a[i]>p[i-1]:
            p.append(a[i])
            i+=1
        elif a[i]==p[i-1]:
            j=i
            while j<n and a[j]==p[i-1]:
                p.append(se.pop(0))
                j+=1
            i=j
        else:
            
            p.append(p[i-1])
            i+=1
        
    dp=[a[0]]
    #print(se,p)
    if len(se)==0:
        
        for i in range(1,n):
            dp.append(max(dp[i-1],p[i]))
    #print(se)
    if dp==a and len(se)==0:
        print(*p)
    else:
        print(-1)