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.

Input

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 $10^5$.

Output

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

见题面 Input 部分

见题面 Output 部分