Bob has just learned hash in today's lesson. A hash function is any function that can be used to map data of arbitrary size to data of fixed size. As a beginner, Bob simply chooses a hash table of size n with hash function h(x) = x % n.

Unfortunately, the hash function may map two distinct value to the same hash value. For example, when n = 9 we have h(7) = h(16) = 7. It will cause a failure in the procession of insertion. In this case, Bob will check whether the next position (h(x) + 1) % n is available or not. This task will not be finished until an available position is found. If we insert {7, 8, 16} into a hash table of size 9, we will finally get {16, -1, -1, -1, -1, -1, -1, 7, 8}. Available positions are labeled as -1.

After done all the exercises, Bob became curious to the inverse problem. Can we rebuild the insertion sequence from a hash table? If there are multiple available insertion sequences, Bob will just select the smallest one under lexicographical order.

{a₁, a₂, .., a_n} is lexicographically smaller than {b₁, b₂, .., b_n} if and only if there exists i (1 ≤ i ≤ n) satisfy that a_i < b_i and a_j = b_j (1 ≤ j < i).

There are multiple cases.
The first line of input is an integer T (1 ≤ T ≤ 20) which indicates the cases of test data.
The first line of each case contains a positive integer n (1 ≤ n ≤ 10⁵). The second line contains exactly n numbers a_i (-1 ≤ a_i ≤ 10⁸).
It is guaranteed for each test cases that at least one available insertion sequences exist.

For each case, please output smallest available insertion sequence in a single line. Print an empty line when the available insertion sequence is empty.