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:
kl = int(input())
for l in range(kl):

    n = int(input())
    t = n * 2
    at = list(range(t + 1))
    nl = [1] * t
    b = []
    rz = []
    pr = 0
    #    print(nl)
    #    print(at)
    for i in input().split():
        i = int(i)
        nl[i - 1] = 0
        b = b + [i]
    #    print(nl)
    #    print(b)
    for i in range(n):
        if pr:
            break
        pr = 1
        #        print(b[i], t)
        #        print(at)
        #        print(nl)

        for j in range(b[i], t + 1):
            if at[j] * nl[j - 1] != 0:
                nl[j - 1] = 0
                rz = rz + [b[i]] + [at[j]]
                pr = 0
                break
    #    print(nl)
    #    print(b)
    #    print(rz)
    if pr:
        print(-1)
    else:
        for i in range(t):
            print(rz[i], '', end='')