Problem: You are given a sequence b_1, b_2, …, b_n. Find the lexicographically minimal permutation a_1, a_2, …, a_{2n} such that b_i = min(a_{2i-1}, a_{2i}), or determine that it is impossible.

Input

Each test contains one or more test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100).

The first line of each test case consists of one integer n — the number of elements in the sequence b (1 ≤ n ≤ 100).

The second line of each test case consists of n different integers b_1, …, b_n — elements of the sequence b (1 ≤ b_i ≤ 2n).

It is guaranteed that the sum of n by all test cases doesn't exceed 100.

Output

For each test case, if there is no appropriate permutation, print one number -1.

Otherwise, print 2n integers a_1, …, a_{2n} — required lexicographically minimal permutation of numbers from 1 to 2n.

Example

Input


5
1
1
2
4 1
3
4 1 3
4
2 3 4 5
5
1 5 7 2 8


Output


1 2 
-1
4 5 1 2 3 6 
-1
1 3 5 6 7 9 2 4 8 10 

Solution (in PYTHON3):

Solution:
t=int(input())
for i in range(t):
    op=[]
    n=int(input())
    x=list(input().split())
    xi=[int(i) for i in x]
    for j in range(2*n):
        if j%2==0:
            t=xi[j//2]
            op.append(t)
        else:
            op.append(0)
    xx=1
    for j in range(n):
        z=op[xx-1]+1
        if z in op:
            for q in range(z+1,(2*n+1)):
                if q not in op:
                    op[xx]=q
                    break
        else:
            op[xx]=z
        xx+=2
    if max(op)>(2*n):
        print("-1")
    elif 0 in op:
        print("-1")
    else:
        for j in range(len(op)):
            print(op[j],end=" ")
        print()