I. The Art of Rearrangement
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Given an array $$$a$$$ of length $$$n$$$, please rearrange the elements of $$$a$$$ such that the values $$$a_i - i$$$ are pairwise distinct over all $$$1 \leq i \leq n$$$.

Input

The first line contains a single integer $$$t$$$ $$$(1\le t\le 10^{5})$$$ — the number of test cases.

For each test case, the first line contains a single integer $$$n$$$ $$$(2 \le n \le 10^{5})$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ $$$(1\le a_i \le 10^{5})$$$ — the elements of the array.

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

Output

For each test case, print $$$n$$$ integers — a valid rearrangement of the array, or $$$-1$$$ if no such rearrangement exists. If there are multiple solutions, output any.

Example
Input
3
4
1 7 3 5
2
6 4
3
2 3 4
Output
1 3 5 7
4 6
2 4 3
Note

In the first test case, one valid rearrangement of the array is $$$[1, 3, 5, 7]$$$. Because, the differences are: $$$[a_1 - 1, a_2 - 2, a_3 - 3, a_4 - 4]$$$ $$$=$$$ $$$[0, 1, 2, 3]$$$. All of them are distinct.