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:
t=int(input())
for i in range(t):
    n=int(input())
    ans=[0 for i in range(n)]
    a=list(map(int,input().split()))
    if a[-1]!=n:
        print(-1)
    else:
        prtnt=False
        cur=n+1
        #ans[-1]=n
        pos=-1
        posval=0
        used=set()
        counter=1
        counterlim=a[0]
 #       print(ans)
        for i in range(len(a)):
            cur,prev=a[i],cur
            if cur!=prev:
                ans[i]=cur
               # print(ans)
                if counter-1>cur:
                    prtnt=True
                counterlim=cur
                used.add(cur)
            else:
                while counter in used:
                    counter+=1
                ans[i]=counter
                if counter>counterlim:
                    prtnt=True
                counter+=1
               # if counter<1 and i!=0:
               #     print(-1)
              #      prtnt=True
 #           #print(ans,33333)
    #    for i in range(len(a)-2,-1,-1):
           # cur,prev=a[i],cur
           # if cur!=prev:
           #     ans[i]=cur
           #$     counter=min(cur-1,counter)
         #   if ans[i]==0:
      #          ans[i]=counter
       #         counter-=1
       #         if counter<1 and i!=0:
        #            print(-1)
         #           prtnt=True
        if not prtnt:
            print(' '.join(map(str,ans)))
        else:
            print(-1)