Statement : B. Move Back at a Cost

You are given an array of integers $a$ of length $n$. You can perform the following operation zero or more times:

• In one operation choose an index $i$ ($1 \le i \le n$), assign $a_i := a_i + 1$, and then move $a_i$ to the back of the array (to the rightmost position). For example, if $a = [3, 5, 1, 9]$, and you choose $i = 2$, the array becomes $[3, 1, 9, 6]$.

Find the lexicographically smallest$^{\text{∗}}$ array you can get by performing these operations.

$^{\text{∗}}$An array $c$ is lexicographically smaller than an array $d$ if and only if one of the following holds:

• $c$ is a prefix of $d$, but $c \ne d$; or

• in the first position where $c$ and $d$ differ, the array $c$ has a smaller element than the corresponding element in $d$.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line contains a single integer $n$ ($1 \le n \le 10^5$), the length of the array.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$), the elements of the array.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.

For each test case, print the lexicographically smallest array you can get.

Input

3
3
2 1 3
5
1 2 2 1 4
6
1 2 3 6 5 4

Output

1 3 3
1 1 3 3 5
1 2 3 4 6 7