Permutation recovery

Description:

Input:

The first line contains one integer $$$t$$$ — the number of test cases ($$$1 \leq t \leq 100\,000$$$).

Next $$$2 \cdot t$$$ lines contains the description of test cases,two lines for each. The first line contains one integer $$$n$$$ — the length of the permutation, written by Vasya ($$$1 \leq n \leq 500\,000$$$). The second line contains $$$n$$$ integers $$$next_1, next_2, \ldots, next_n$$$, separated by spaces ($$$next_i = -1$$$ or $$$i < next_i \leq n + 1$$$).

It is guaranteed, that the sum of $$$n$$$ in all test cases doesn't exceed $$$500\,000$$$.

In hacks you can only use one test case, so $$$T = 1$$$.

Output:

Print $$$T$$$ lines, in $$$i$$$-th of them answer to the $$$i$$$-th test case.

If there is no such permutations $$$p_1, p_2, \ldots, p_n$$$ of integers from $$$1$$$ to $$$n$$$, that Vasya could write, print the only number $$$-1$$$.

In the other case print $$$n$$$ different integers $$$p_1, p_2, \ldots, p_n$$$, separated by spaces ($$$1 \leq p_i \leq n$$$). All defined values of $$$next_i$$$ which are not equal to $$$-1$$$ should be computed correctly $$$p_1, p_2, \ldots, p_n$$$ using defenition given in the statement of the problem. If there exists more than one solution you can find any of them.

Sample Input:

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

Sample Output:

1 2 3
2 1
2 1 3
-1
1
3 2 1 4

Note:

In the first test case for permutation $$$p = [1, 2, 3]$$$ Vasya should write $$$next = [2, 3, 4]$$$, because each number in permutation is less than next. It's easy to see, that it is the only satisfying permutation.

In the third test case, any permutation can be the answer because all numbers $$$next_i$$$ are lost.

In the fourth test case, there is no satisfying permutation, so the answer is $$$-1$$$.