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:
for w in range(int(input())):
    n=int(input())
    q=list(map(int,input().split()))
    l=[0]*n 
    count=[0]*(n+1)
    c=0
    t=0
    if(n==1):
        if(q[0]==1):
            print(1)
        else:
            print(-1)
    else:
        l[0]=q[0]
        count[q[0]]=1
        for i in range(1,n):
            if(q[i]!=q[i-1]):
                l[i]=q[i]
                count[q[i]]=1
                if(i==1):
                 for j in range(max(t,1),n+1):
                    if(count[j]==0):
                        t=j
                        break
                else:
                    if(l[i]==t):
                      for j in range(max(t,1),n+1):
                       if(j!=0 and count[j]==0):
                        t=j
                        break
            else:
                if(t<q[i]):
                  if(t>0 and count[t]==0):
                    count[t]=1
                    l[i]=t 
                    for j in range(max(t,1),q[i]):
                     if(count[j]==0):
                        t=j
                        break
                  else:
                    t1=t
                    for j in range(max(t,1),q[i]):
                     if(count[j]==0):
                        t=j
                        break
                    if(t!=t1):
                        count[t]=1
                        l[i]=t 
                    else:
                        c=1
                        break
                else:
                    c=1
                    break
        if(c==1):
            print(-1)
        else:
            for i in range(n):
                print(l[i],end=" ")
            print()