Order

There is a sequence $S = (s_1, s_2, \dots, s_n)$ made up of $n$ distinct integers. It is a permutation that uses each integer from $1$ to $n$ exactly once, so $s_i \ne s_j$ for every $i \ne j$ and $1 \le s_i \le n$.

From $S$ we can build a new sequence $R = (r_1, r_2, \dots, r_n)$, where $r_i$ is the number of elements among those that come before $s_i$, namely $\{s_1, s_2, \dots, s_{i-1}\}$, that are smaller than $s_i$.

For example, if $n = 10$ and $S = (6, 4, 3, 5, 1, 2, 7, 8, 9, 10)$, then $R = (0, 0, 0, 2, 0, 1, 6, 7, 8, 9)$.

Given a sequence $R$, write a program that recovers the original sequence $S$. If an $S$ corresponding to $R$ exists, it is uniquely determined, but for some inputs no such $S$ exists. For example, if $n = 5$ and $R = (0, 2, 2, 0, 1)$, then no $S$ corresponds to this $R$.

Input is read from standard input. The first line contains the number of test cases $T$. Each test case consists of two lines: the first line contains the length of the sequence $n$ ($1 \le n \le 100$), and the second line contains the $n$ integers $r_1, r_2, \dots, r_n$ of the sequence $R$, separated by spaces.

For each test case, print the sequence $S$ corresponding to the given $R$ on one line, with its numbers separated by spaces. If $S$ cannot be recovered from $R$, print IMPOSSIBLE on that line instead.